These are 8 questions and 8 answers:
1) Quesion 1:
9+√2
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4 - √7
Answer: the third option:
36 + 9√7 + 4√2 + √14
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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.
