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Answer:

Q. 1

Note that x = 9. Plug in 9 for x.

√(x + 7) = √(9 + 7)

Simplify. Add, then root

√(9 + 7) = √16 = √(4 * 4) = 4

4, or (B) is your answer

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Q. 2

Note that x = 16. Plug in 16 for x

√(x + 20) = √(16 + 20)

Simplify. Add, then root.

√(16 + 20) = √36 = √(6 * 6) = 6

6, or (D) is your answer

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Q. 3

Note that x = 9. Plug in 9 for x.

3 + √(9 + 7) - √(3(9))

Simplify. Combine the terms. Remember to follow PEMDAS.

3 + √(16) - √(27)

3 + 4 - 3√3

Simplify to get the final answer. Note that you can only combine terms with the same amount for roots

(3 + 4) - 3√3

7 - 3√3, or (C) is your answer

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Q. 4

Note that x = 6. Plug in 6 for x.

√(24 - (6))

Simplify. First solve the parenthesis

√(24 - 6) = √(18)

Simplify. Change the root to a decimal.

√18 = √( 3 * 3 * 2) = ~4.24

4.24, or (A) is your answer

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Q. 5

Note that x = 2. Plug in 2 for x in the expression.

6 + √(14 + x) - √(9x)

6 + √(14 + 2) - √(9(2)

Simplify. Follow PEMDAS. First, simplify the parenthesis

6 + √(16) - √18

Next, simplify the roots

6 + 4 - 3√2

Simplify. Combine like terms

(6 + 4) - 3√2

10 - 3√2

Change to decimal

- 3√2 ≈ -4.24

Subtract

10 - 4.24 = 5.76

5.76 or (C) is your answer

~

gmany

Put the values of x to the expreesions.

[tex]\sqrt{a}=b\iff b^2=a[/tex]

[tex]Q1.\\x=9\\\\\sqrt{x+7}=\sqrt{9+7}=\sqrt{16}=\boxed{4}\ \text{because}\ 4^2=16\\\\Q2.\\x=16\\\\\sqrt{x+20}=\sqrt{16+20}=\sqrt{36}=\boxed{6}\ \text{because}\ 6^2=36\\\\Q3.\\x=9\\\\\sqrt{x+7}=\sqrt{7+9}=\sqrt{16}=4\ \text{because}\ 4^2=16\\\sqrt{3x}=\sqrt{3\cdot9}=\sqrt9\cdot\sqrt3=3\sqrt3;\ \sqrt9=3\ \text{because}\ 3^2=9\\\\3+\sqrt{x+7}-\sqrt{3x}=3+4-3\sqrt3=\boxed{7-3\sqrt3}\\\\Q4.\\x=6\\\\\sqrt{24-x}=\sqrt{24-6}=\sqrt{18}=\sqrt{9\cdot2}=\sqrt9\cdot\sqrt2=\boxed{3\sqrt2}\approx\boxed{4.24}[/tex]

[tex]Q5.\\x=2\\\\\sqrt{14+x}=\sqrt{14+2}=\sqrt{16}=4\\\sqrt{9x}=\sqrt{9\cdot2}=\sqrt9\cdot\sqrt2=3\sqrt2\\\\6+\sqrt{14+x}-\sqrt{9x}=6+4-3\sqrt2=\boxed{10-3\sqrt2}\approx\boxed{5.76}[/tex]


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