Solve Square Root Expression: √36 × √49 + 7² × 2

Q: Do I need to memorize perfect square roots like √36 and √49?

Yes! Knowing perfect squares 1-12 makes calculations much faster. Practice: $ \sqrt{1}=1, \sqrt{4}=2, \sqrt{9}=3, \sqrt{16}=4 $, etc.

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

Mathematics follows PEMDAS order, not reading order! You must do all multiplications and exponents before addition, even if addition appears first in the expression.

Q: What if I calculated √36 × √49 as √(36 × 49) instead?

That's actually correct too! $ \sqrt{36} \times \sqrt{49} = \sqrt{36 \times 49} = \sqrt{1764} = 42 $. Both methods give the same answer.

Q: How do I remember to do 7² × 2 before adding?

Think PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Since $ 7^2 $ is an exponent and multiplication comes before addition, do $ 7^2 \times 2 = 98 $ first.

Q: Can I use a calculator for the square roots?

Practice without first! Perfect squares like 36 and 49 should become automatic. Calculators are helpful for checking, but understanding the concept is more important.

Square Roots with Order Operations

$\sqrt{36}\times\sqrt{49}+7^2\times2=$

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Step-by-step written solution

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Understand the problem

$\sqrt{36}\times\sqrt{49}+7^2\times2=$

Step-by-step solution

The given expression is: $\sqrt{36}\times\sqrt{49}+7^2\times2$ .

First, calculate the square roots: $\sqrt{36} = 6$ and $\sqrt{49} = 7$ .

Multiply the square roots: $6 \times 7 = 42$ .

Next, calculate the square: $7^2 = 49$ .

Multiply the result by 2: $49 \times 2 = 98$ .

Finally, add the two results: $42+98=140$ .

Thus, the answer is: $140$ .

Final Answer

140

Key Points to Remember

Essential concepts to master this topic

Square Roots: Calculate $\sqrt{36} = 6$ and $\sqrt{49} = 7$ first
Order of Operations: Multiply and square before adding: $6 \times 7 = 42$ , then $7^2 \times 2 = 98$
Final Check: Add results in correct order: $42 + 98 = 140$ ✓

Common Mistakes

Avoid these frequent errors

Adding before multiplying all terms
Don't calculate $\sqrt{36} + \sqrt{49} = 6 + 7 = 13$ first = wrong order! This ignores multiplication and gives incorrect results like 182. Always follow PEMDAS: calculate all multiplications and exponents before adding.

Practice Quiz

Test your knowledge with interactive questions

$5+\sqrt{36}-1=$

FAQ

Everything you need to know about this question

Do I need to memorize perfect square roots like √36 and √49?

Yes! Knowing perfect squares 1-12 makes calculations much faster. Practice: $\sqrt{1}=1, \sqrt{4}=2, \sqrt{9}=3, \sqrt{16}=4$ , etc.

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

Mathematics follows PEMDAS order, not reading order! You must do all multiplications and exponents before addition, even if addition appears first in the expression.

What if I calculated √36 × √49 as √(36 × 49) instead?

That's actually correct too! $\sqrt{36} \times \sqrt{49} = \sqrt{36 \times 49} = \sqrt{1764} = 42$ . Both methods give the same answer.

How do I remember to do 7² × 2 before adding?

Think PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Since $7^2$ is an exponent and multiplication comes before addition, do $7^2 \times 2 = 98$ first.

Can I use a calculator for the square roots?

Practice without first! Perfect squares like 36 and 49 should become automatic. Calculators are helpful for checking, but understanding the concept is more important.

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