Q. \(7^2 + 9^2\).

Q: How do you compute 7^2 and 9^2 mentally?

Use known squares or near-square tricks: 7^2=49. For 9^2, use (10-1)^2=100-20+1=81. Then add 49+81=130.

Q: Is 130 a perfect square?

No. 11^2=121 and 12^2=144, so 130 is between them and not a perfect square.

Q: What is \sqrt{130} and can it be simplified?.

\sqrt{130}=\sqrt{10\cdot13}; it does not simplify to an integer or simpler surd. Numerically \sqrt{130}\approx11.4018..

Q: Can 7,9, and \sqrt{130} be the sides of a right triangle?.

Yes: 7^2+9^2=130, so the hypotenuse would be \sqrt{130}. It’s a right triangle but not a Pythagorean triple (hypotenuse is not an integer)..

Q: What is the prime factorization of 130?.

What is the prime factorization of 130?.

Q: Are there other integer pairs whose squares sum to 130?

Yes: besides 7^2+9^2, we have 11^2+3^2=121+9=130. Up to order and signs those are the integer representations..

Q: Is 130 even or odd and is it divisible by 5 or 13?.

130 is even (2 divides it) and divisible by 5 and 13; 130/5=26, 130/13=10..

Answer

\[
7^2 + 9^2 = 49 + 81 = 130
\]

Detailed Explanation

Write the expression to evaluate: \(7^2+9^2\). Here, \(n^2\) means \(n\) multiplied by itself.
Compute the first square: \(7^2=7\times7=49\).
Compute the second square: \(9^2=9\times9=81\).
Add the two results: \(49+81=130\).
Final answer: \(7^2+9^2=130\).

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Arithmetic FAQs

What is \(7^2+9^2\)?.

\(7^2+9^2=49+81=130\)..

How do you compute \(7^2\) and \(9^2\) mentally?

Use known squares or near-square tricks: \(7^2=49\). For \(9^2\), use \((10-1)^2=100-20+1=81\). Then add \(49+81=130\).

Is \(130\) a perfect square?

No. \(11^2=121\) and \(12^2=144\), so \(130\) is between them and not a perfect square.

What is \( \sqrt{130} \) and can it be simplified?.

\(\sqrt{130}=\sqrt{10\cdot13}\); it does not simplify to an integer or simpler surd. Numerically \(\sqrt{130}\approx11.4018\)..

Can \(7,9,\) and \(\sqrt{130}\) be the sides of a right triangle?.

Yes: \(7^2+9^2=130\), so the hypotenuse would be \(\sqrt{130}\). It’s a right triangle but not a Pythagorean triple (hypotenuse is not an integer)..

What is the prime factorization of \(130\)?.

Are there other integer pairs whose squares sum to \(130\)?

Yes: besides \(7^2+9^2\), we have \(11^2+3^2=121+9=130\). Up to order and signs those are the integer representations..

Is \(130\) even or odd and is it divisible by 5 or 13?.

\(130\) is even (\(2\) divides it) and divisible by \(5\) and \(13\); \(130/5=26\), \(130/13=10\)..

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