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These are 8 questions and 8 answers:

1) Quesion 1:

 9+√2
---------
 4 - √7

Answer: the third option:

36 + 9√7 + 4√2 + √14
-----------------------------
               9

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator.

The conjugate of 4 - √7 = 4 + √7

=>

[tex] \frac{9+ \sqrt{2} }{4- \sqrt{7} } . \frac{4+ \sqrt{7} }{4+ \sqrt{7} } = \frac{(9)(4)+9 \sqrt{7}+4 \sqrt{2} + \sqrt{2} . \sqrt{7} }{(4)^2-( \sqrt{7})^2 } =[/tex]

[tex]= \frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{16-7} [/tex]

2) Question 2: sum

[tex]5x (\sqrt[3]{x^2y})+2( \sqrt[3]{x^5y})[/tex]

Answer: fourth option

[tex]7x( \sqrt[3]{x^2y} )[/tex]

Explanation:

Take x^5 out of the second radical which will result in a like term of the first radical:

[tex]5x( \sqrt[3]{x^2y} )+2( \sqrt[3]{x^5y}) =5x( \sqrt[3]{x^2y} )+2x( \sqrt[3]{x^2y})=7x( \sqrt[3]{x^2y}) [/tex]

which is the fourth option

3) Question 3. Which expression is equivalent to:

[tex] \frac{ \sqrt{10} }{ \sqrt[4]{8} }[/tex]

Answer: the first option

Explanation

[tex] \frac{ \sqrt{10} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{10^2} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{100} }{ \sqrt[4]{8} } . \frac{ \sqrt[4]{8^3} }{ \sqrt[4]{8^3} } = \frac{ \sqrt[4]{(100)(512)} }{8} = \frac{ \sqrt[4]{51200} }{8} = \frac{4 \sqrt[4]{200} }{8} = \frac{ \sqrt[4]{200} }{2} [/tex]

4) Question 4 What is the simplest form?

Answer: the second option

Explanation:

[tex] \sqrt[4]{81x^8y^5}=x^2 y\sqrt[4]{3^4y} =3x^2y \sqrt[4]{y} [/tex]

5) Question 5 Product

Answer: the fourth option:

[tex]104x^4+16x^4 \sqrt{30} [/tex]

Explanation:

Use the square of a binomial product: (a + b)^2 = a^2 + 2ab + b^2

[tex](4x \sqrt{5x^2} )^2+2(4x \sqrt{5x^2})(2x^2 \sqrt{6}) +(2x^2 \sqrt{6} )^2=[/tex]

[tex]=16x^2(5x^2)+16x^4( \sqrt{30} )+4x^4(6)=80x^4+16x^4 \sqrt{30} +24x^4=[/tex]

[tex]=104x^4+16x^4 \sqrt{30} [/tex]

which is the fourth option.

6) Question 6 Product

Answer: fourth option

Explanation:

[tex] \sqrt[3]{16x^7} . \sqrt[3]{12x^9} = \sqrt[3]{2^4.2^2.3x^7x^9} = \sqrt[3]{2^6.3.x^{16}}=2^2 x^5 \sqrt[3]{3x} =4 x^5\sqrt[3]{3x} [/tex]

which is the fourth option.

7) Question 7. Simplified form of 2√18 + 3√2 + √162

Answer: 18√2

Explanation:

[tex]2 \sqrt{18}+3 \sqrt{2} + \sqrt{162}=2(3) \sqrt{2} + 3 \sqrt{2} +9 \sqrt{2} =18 \sqrt{2} [/tex]

which is the second option.

8) Question 8 which function is undefined for x = 0.

Answer: second option y = √ (x - 2)

Explanation.

The square root function is not defined for negative values.

When x = 0, x - 2 = -2, whose square root is not defined.

Therefore, the square root of x - 2 is not defined for x = 0.

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