Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Module 8 Answer Key The Pythagorean Theorem.

## Texas Go Math Grade 8 Module 8 Answer Key The Pythagorean Theorem

**Texas Go Math Grade 8 Module 8 Are You Ready? Answer Key**

**Find the square of each number.**

Question 1.

5 _________

Answer:

To determine the square of a number x, denoted by x^{2} just multiply the given number x by itself.

Now, let us get the square of 5 or the equivalent of 5^{2}, just multiply 5 by itself, that is

5^{2} = 5 × 5

= 25

or

Question 2.

16 __________

Answer:

When solving for the square of a number, we need to multiply the certain number by itself.

To find the square of 16, we simply multiply it by itself

16^{2} = 16 × 16

= 256

Question 3.

-11 _________

Answer:

To determine the square of a number x, denoted by x^{2} just multiply the given number x by itself.

Now, let us get the square of -11 or the equivalent of (-11)^{2}, just multiply 11 by itself, that is

(-11)^{2} = -11(-11)

= 121

Question 4.

\(\frac{2}{7}\) __________

Answer:

To solve for the square of \(\frac{2}{7}\), we simply multiply it by itself. Take note that in multiplying fractions, the product is equal to the product of all numerators divided by the product of all denominators.

(\(\frac{2}{7}\))^{2} = \(\frac{2}{7}\) × \(\frac{2}{7}\) = \(\frac{4}{49}\)

**Evaluate each expression.**

Question 5.

\(\sqrt{(6+2)^{2}+(3+3)^{2}}\) __________

Answer:

\(\sqrt{(6+2)^{2}+(3+3)^{2}}=\sqrt{8^{2}+6^{2}}\) (First, operate within parentheses.) …… (1)

= \(\sqrt{64+36}\) (Next, simplify exponents.) ………. (2)

= \(\sqrt{100}\) (Then add and subtract left to right.) ……….. (3)

= 10 (Finally, take the square root.) ……… (4)

= 10

Question 6.

\(\sqrt{(9-4)^{2}+(5+7)^{2}}\) __________

Answer:

\(\sqrt{(9-4)^{2}+(5+7)^{2}}=\sqrt{5^{2}+12^{2}}\) (First, operate within parentheses.) …… (1)

= \(\sqrt{25+144}\) (Next, simplify exponents.) ………. (2)

= \(\sqrt{169}\) (Then add and subtract left to right.) ……….. (3)

= 13 (Finally, take the square root.) ……… (4)

= 13

Question 7.

\(\sqrt{(10-6)^{2}+(15-12)^{2}}\) __________

Answer:

\(\sqrt{(10-6)^{2}+(15-12)^{2}}=\sqrt{4^{2}+3^{2}}\) (First, operate within parentheses.) …… (1)

= \(\sqrt{16+9}\) (Next, simplify exponents.) ………. (2)

= \(\sqrt{25}\) (Then add and subtract left to right.) ……….. (3)

= 5 (Finally, take the square root.) ……… (4)

= 5

Question 8.

\(\sqrt{(6+9)^{2}+(10-2)^{2}}\) __________

Answer:

\(\sqrt{(6+9)^{2}+(10-2)^{2}}=\sqrt{15^{2}+8^{2}}\) (First, operate within parentheses.) …… (1)

= \(\sqrt{225+64}\) (Next, simplify exponents.) ………. (2)

= \(\sqrt{289}\) (Then add and subtract left to right.) ……….. (3)

= 17 (Finally, take the square root.) ……… (4)

= 17

**Simplify each expression.**

Question 9.

5(8)(10) ___________

Answer:

5(8)(10) = (40)(10) (Multiply from left to right)

= 400

Question 10.

\(\frac{1}{2}\)(6)(12) ___________

Answer:

\(\frac{1}{2}\)(6)(12) = (3)(12) (Multiply from left to right)

= 36

Question 11.

\(\frac{1}{3}\)(3)(12) ___________

Answer:

\(\frac{1}{3}\)(3)(12) = (1)(12) (Multiply from left to right)

= 12

Question 12.

\(\frac{1}{2}\)(8^{2})(4) ___________

Answer:

Simplify expression

\(\frac{1}{2}\)(8^{2})(4) = \(\frac{1}{2}\)(64)(4) (Simplify the exponent) …………. (1)

= (32)(4) (Multiply from left to right) ……………… (2)

= 128

Question 13.

\(\frac{1}{4}\)(10)^{2}(15) ___________

Answer:

Simplify expression

\(\frac{1}{4}\)(10^{2})(15) = \(\frac{1}{4}\)(100)(15) (Simplify the exponent) …………. (1)

= (25)(15) (Multiply from left to right) ……………… (2)

= 375

Question 14.

\(\frac{1}{3}\)(9)^{2}(6) ___________

Answer:

Simplify expression

\(\frac{1}{3}\)(9^{2})(6) = \(\frac{1}{3}\)(81)(6) (Simplify the exponent) …………. (1)

= (27)(6) (Multiply from left to right) ……………… (2)

= 162

**Texas Go Math Grade 8 Module 8 Reading Start-Up Answer Key**

**Visualize Vocabulary**

Use the ✓ words to complete the graphic.

**Understand Vocabulary**

Match the term on the left to the correct expression on the right.

Answer:

1 – C. Hypotenuse: The side opposite the right angle in a right triangle

2 – A. Theorem: An idea that has been demonstrated as true.

3 – B. Legs: The two sides that form the right angle of a right triangle.

**Active Reading**

Booklet Before beginning the module, create a booklet to help you learn about the Pythagorean Theorem. Write the main idea of each lesson on each page of the booklet. As you study each lesson, write important details that support the main idea, such as vocabulary and formulas. Refer to your finished booklet as you work on assignments and study for tests.