How to evaluate (3 + 5)² quickly and clearly

If you’ve ever looked at a simple expression and felt a little lights-out moment, you’re not alone. Math sometimes feels like a tiny machine: feed in something inside parentheses, then crank up the power with an exponent. On the HSPT math side, these two moves show up again and again. So let’s walk through a classic example and keep the gears moving smoothly.

The question at a glance

Here’s a tidy one that pops up often:

What is the value of (3 + 5)²?

A. 54

B. 64

C. 72

D. 36

The correct answer is 64. Let me explain how you get there without getting tangled in the steps.

Step-by-step through the punch line

First, the numbers inside the parentheses get added:

3 + 5 = 8.

Then, that result gets squared (multiplied by itself):

8² = 8 × 8 = 64.

So, (3 + 5)² equals 64. Simple, right? But the value comes from following the right order of operations: parentheses first, then the exponent. If you forget one of those steps, you’ll stumble.

Two ways to see it, and why both help

Sometimes it helps to see the same idea in a slightly different light:

• The straightforward way: add inside the parentheses, then square. That’s the rhythm you’ll use most often.

• The expansion shortcut (handy if you want to check your answer): use the formula (a + b)² = a² + 2ab + b². If a = 3 and b = 5, you get 3² + 2·3·5 + 5² = 9 + 30 + 25 = 64. Either path lands you on the same result.

That second approach is like a quick consistency check. It’s not always needed, but it’s a nice safety net when you’re unsure about the steps.

Why this concept matters beyond one problem

You’ll see problems like this a lot in the HSPT math section because they test your comfort with structure. It’s not just about the numbers; it’s about recognizing the pattern:

• You’re asked to evaluate expressions, not just spit out a random number.

• The key is to trust the order in which operations happen. If you treat the expression as a single blur of actions, you’ll miss the point.

• Exponents, especially with sums inside parentheses, show up in varied forms. Some versions ask you to expand, others to compare results, still others to apply the idea to real-world contexts like area or growth rates.

Common pitfalls to dodge

Even seasoned students slip on a few easy traps. Here are the ones that tend to trip people up with expressions like this:

• Forgetting to do the inside work first. If you square 3 and 5 separately before adding, you’ll get the wrong result.

• Thinking that squaring a sum means squaring each addend and adding results (that’s not the rule here).

• Confusing (a + b)² with a² + b². The middle term 2ab matters a lot.

• Skipping a quick expansion check when the numbers get a bit bigger. A tiny algebraic nudge can save you from a misstep.

• Overthinking. This isn’t meant to be a trick question; it’s about applying the rules clearly.

Smart habits you can carry forward

Here are some easy, practical habits that help with these kinds of problems, without turning you into a math robot:

• Read the expression out loud in your head. Pause at the parentheses, then at the exponent. The rhythm helps you catch the important steps.

• When in doubt, do a quick check using the expansion idea. If the numbers are friendly, the check is a quick sanity test.

• Write a tiny plan before you compute. A simple “1) add inside parentheses, 2) square result” can keep you on track.

• Practice with small variations to see the pattern: (2 + 4)², (7 + 1)², or even (1 + 1)². Each one reinforces the same rule.

A couple more friendly prompts

If you want to cement the idea with a couple more light-weight examples, try these and use the same approach:

• What’s (2 + 3)²? Follow the steps: 2 + 3 = 5, 5² = 25. So the answer is 25.

• How about (6 + 2)²? First, 6 + 2 = 8, then 8² = 64.

• One more twist: (1 + 9)². Inside adds to 10, and 10² = 100.

Each time, the structure is the same. Your comfort grows as the pattern repeats, and suddenly you’re not thinking about the steps as much as you’re letting the steps flow.

Bringing it back to everyday math

This isn’t just about tests. It mirrors how you reason through problems in real life, too. Suppose you’re planning a small project with a couple of steps, like combining two ingredients and then measuring the total amount raised to a power of something—okay, that’s a little silly, but you get the idea. The underlying habit is universal: handle the inside first, then apply the broader operation. In math and in many daily tasks, that order keeps things predictable and reliable.

Real-world metaphors that click

Speaking of reliable, think of it like mixing paints. If you pour blue and yellow into a cup, you first blend them to see the new color—inside the cup, the sum, if you will. Only after you’ve got that blended color do you decide how light or dark to make it; that’s the analog of squaring in our expression. The “square” acts like an amplification of whatever you’ve just created. The smoother you master this sequence, the more intuitive it becomes, whether you’re solving a math problem or balancing a budget.

A short detour that stays on track

Some learners worry about whether to memorize every algebraic identity. It’s fine to know general forms, but in these scenarios, it’s more about recognizing the steps and keeping them straight. When you see a sum inside parentheses followed by a superscript, you’re almost always looking at two moves: compute inside, then apply the exponent. The pattern is your friend, not a trap.

Putting it all together, with a handy little recap

• Identify the operations in the correct order: inside parentheses first, then the exponent.

• Compute the sum inside the parentheses.

• Apply the square to that sum.

• If you want extra assurance, expand using (a + b)² = a² + 2ab + b² and plug in the numbers.

• Check against common mistakes to keep your reasoning tight.

Balancing clarity with curiosity

One nice thing about math is that it rewards curiosity in small doses. If a concept feels dry at first, try turning it into a tiny puzzle you solve in your own words. Ask yourself: What happens if I change the numbers? Does the order of operations still hold? How would I explain this to a friend who’s new to the idea? Those little explorations keep you engaged and make recall easier when you hit similar problems again.

A few pointers for broader study harmony

• Mix a handful of problems like this with slightly different structures to prevent tunnel vision.

• Use a simple scratch work routine: write the inner sum, then the outer operation. A clean chain of steps is a clean mind.

• When you stumble, pause. Rephrase the problem verbally, then re-approach with the plan in mind.

Final takeaway

Expressions like (3 + 5)² aren’t tests of brute force; they’re tests of a reliable method. By keeping the order of operations front and center, you translate a tiny mental puzzle into a clear, confident result. In this case, 64 is the payoff, and it’s the product of a simple (and very human) rule: handle the inside, then power it up.

If you’re curious to see how this rule plays with other numbers, try a few variations on your own. You’ll start spotting the pattern, and soon the feeling of “I’ve got this” will show up sooner, not later. After all, math isn’t about memorizing a single answer; it’s about building a way of thinking that you can carry into any problem that comes your way. And that, in the end, feels pretty empowering.