Solve: Square Root of 4 Times 4 Squared Minus 5 Squared

Q: Which operations should I do first in this problem?

Start with roots and exponents first! Calculate $ \sqrt{4} = 2 $, $ 4^2 = 16 $, $ 5^2 = 25 $, and $ \sqrt{1} = 1 $ before doing any multiplication or subtraction.

Q: Why can't I just work from left to right?

The order of operations (PEMDAS) requires specific steps! If you work left to right, you'll get wrong answers. Always follow: Parentheses, Exponents/Roots, Multiplication/Division, Addition/Subtraction.

Q: What's the difference between √4 and 4²?

$ \sqrt{4} $ means what number times itself equals 4? Answer: 2. But $ 4^2 $ means 4 times 4, which equals 16. They're opposite operations!

Q: How do I handle the multiplication after finding the roots and exponents?

Once you have $ 2 \times 16 - 25 \times 1 $, do both multiplications first: $ (2 \times 16) - (25 \times 1) = 32 - 25 = 7 $.

Q: Is √1 really just 1?

Yes! $ \sqrt{1} = 1 $ because 1 × 1 = 1. This is one of the basic square roots you should memorize along with $ \sqrt{4} = 2 $, $ \sqrt{9} = 3 $, etc.

Order of Operations with Roots and Exponents

Solve:

$\sqrt{4}\cdot4^2-5^2\cdot\sqrt{1}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:05 Always calculate roots and exponents first

00:08 An exponent is actually the number multiplied by itself as many times as the power

00:11 Break down each exponent into multiplications and solve

00:24 The root of 1 is always equal to 1

00:29 Always solve multiplication and division before addition and subtraction

00:36 That's the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve:

$\sqrt{4}\cdot4^2-5^2\cdot\sqrt{1}$

Step-by-step solution

We simplify each term according to the order from left to right:

$\sqrt{4}=2$

$4^2=4\times4=16$

$5^2=5\times5=25$

$\sqrt{1}=1$

Now we rearrange the exercise accordingly:

$2\times16-25\times1$

Since there are two multiplication operations in the exercise, according to the order of operations we start with them and then subtract.

We put the two multiplication exercises in parentheses to avoid confusion during the solution, and solve from left to right:

$(2\times16)-(25\times1)=32-25=7$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Evaluate roots and exponents before multiplication and subtraction
Technique: Calculate $\sqrt{4} = 2$ and $4^2 = 16$ first
Check: Verify $2 \times 16 - 25 \times 1 = 32 - 25 = 7$ ✓

Common Mistakes

Avoid these frequent errors

Calculating operations from left to right without following order of operations
Don't just work left to right like √4·4²-5²·√1 = 2·16-25·1 = 32-25-1 = 6! This ignores proper order and gives wrong answers. Always evaluate roots and exponents first, then handle multiplication and subtraction according to PEMDAS.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Which operations should I do first in this problem?

Start with roots and exponents first! Calculate $\sqrt{4} = 2$ , $4^2 = 16$ , $5^2 = 25$ , and $\sqrt{1} = 1$ before doing any multiplication or subtraction.

Why can't I just work from left to right?

The order of operations (PEMDAS) requires specific steps! If you work left to right, you'll get wrong answers. Always follow: Parentheses, Exponents/Roots, Multiplication/Division, Addition/Subtraction.

What's the difference between √4 and 4²?

$\sqrt{4}$ means what number times itself equals 4? Answer: 2. But $4^2$ means 4 times 4, which equals 16. They're opposite operations!

How do I handle the multiplication after finding the roots and exponents?

Once you have $2 \times 16 - 25 \times 1$ , do both multiplications first: $(2 \times 16) - (25 \times 1) = 32 - 25 = 7$ .

Is √1 really just 1?

Yes! $\sqrt{1} = 1$ because 1 × 1 = 1. This is one of the basic square roots you should memorize along with $\sqrt{4} = 2$ , $\sqrt{9} = 3$ , etc.

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