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
=>
2) Question 2: sum
![5x (\sqrt[3]{x^2y})+2( \sqrt[3]{x^5y})](https://tex.z-dn.net/?f=5x%20%28%5Csqrt%5B3%5D%7Bx%5E2y%7D%29%2B2%28%20%5Csqrt%5B3%5D%7Bx%5E5y%7D%29)
Answer: fourth option
![7x( \sqrt[3]{x^2y} )](https://tex.z-dn.net/?f=7x%28%20%5Csqrt%5B3%5D%7Bx%5E2y%7D%20%29)
Explanation:
Take x^5 out of the second radical which will result in a like term of the first radical:
![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})](https://tex.z-dn.net/?f=5x%28%20%5Csqrt%5B3%5D%7Bx%5E2y%7D%20%29%2B2%28%20%5Csqrt%5B3%5D%7Bx%5E5y%7D%29%20%3D5x%28%20%5Csqrt%5B3%5D%7Bx%5E2y%7D%20%29%2B2x%28%20%5Csqrt%5B3%5D%7Bx%5E2y%7D%29%3D7x%28%20%5Csqrt%5B3%5D%7Bx%5E2y%7D%29%20%20)
which is the fourth option
3) Question 3. Which expression is equivalent to:
![\frac{ \sqrt{10} }{ \sqrt[4]{8} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B10%7D%20%7D%7B%20%5Csqrt%5B4%5D%7B8%7D%20%7D)
Answer: the first option
Explanation
![\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}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B10%7D%20%7D%7B%20%5Csqrt%5B4%5D%7B8%7D%20%7D%20%3D%20%5Cfrac%7B%20%5Csqrt%5B4%5D%7B10%5E2%7D%20%7D%7B%20%5Csqrt%5B4%5D%7B8%7D%20%7D%20%3D%20%5Cfrac%7B%20%5Csqrt%5B4%5D%7B100%7D%20%7D%7B%20%5Csqrt%5B4%5D%7B8%7D%20%7D%20.%20%20%5Cfrac%7B%20%5Csqrt%5B4%5D%7B8%5E3%7D%20%7D%7B%20%5Csqrt%5B4%5D%7B8%5E3%7D%20%7D%20%20%3D%20%5Cfrac%7B%20%5Csqrt%5B4%5D%7B%28100%29%28512%29%7D%20%7D%7B8%7D%20%3D%20%5Cfrac%7B%20%5Csqrt%5B4%5D%7B51200%7D%20%7D%7B8%7D%20%3D%20%5Cfrac%7B4%20%5Csqrt%5B4%5D%7B200%7D%20%7D%7B8%7D%20%3D%20%5Cfrac%7B%20%5Csqrt%5B4%5D%7B200%7D%20%7D%7B2%7D%20)
4) Question 4 What is the simplest form?
Answer: the second option
Explanation:
![\sqrt[4]{81x^8y^5}=x^2 y\sqrt[4]{3^4y} =3x^2y \sqrt[4]{y}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81x%5E8y%5E5%7D%3Dx%5E2%20y%5Csqrt%5B4%5D%7B3%5E4y%7D%20%20%3D3x%5E2y%20%5Csqrt%5B4%5D%7By%7D%20)
5) Question 5 Product
Answer: the fourth option:
![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=](https://tex.z-dn.net/?f=104x%5E4%2B16x%5E4%20%5Csqrt%7B30%7D%20%5B%2Ftex%3C%2Fstrong%3E%5D%5C%5C%3Cstrong%3EExplanation%3A%3C%2Fstrong%3E%5C%5CUse%20the%20square%20of%20a%20binomial%20product%3A%20%28a%20%2B%20b%29%5E2%20%3D%20a%5E2%20%2B%202ab%20%2B%20b%5E2%5C%5C%5Btex%5D%284x%20%5Csqrt%7B5x%5E2%7D%20%29%5E2%2B2%284x%20%5Csqrt%7B5x%5E2%7D%29%282x%5E2%20%5Csqrt%7B6%7D%29%20%2B%282x%5E2%20%5Csqrt%7B6%7D%20%29%5E2%3D)
which is the fourth option.
6) Question 6 Product
Answer: fourth option
Explanation:
![\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}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B16x%5E7%7D%20.%20%5Csqrt%5B3%5D%7B12x%5E9%7D%20%3D%20%5Csqrt%5B3%5D%7B2%5E4.2%5E2.3x%5E7x%5E9%7D%20%3D%20%20%5Csqrt%5B3%5D%7B2%5E6.3.x%5E%7B16%7D%7D%3D2%5E2%20x%5E5%20%5Csqrt%5B3%5D%7B3x%7D%20%3D4%20x%5E5%5Csqrt%5B3%5D%7B3x%7D%20)
which is the fourth option.
7) Question 7. Simplified form of 2√18 + 3√2 + √162
Answer: 18√2
Explanation:
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.
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
=>
2) Question 2: sum
Answer: fourth option
Explanation:
Take x^5 out of the second radical which will result in a like term of the first radical:
which is the fourth option
3) Question 3. Which expression is equivalent to:
Answer: the first option
Explanation
4) Question 4 What is the simplest form?
Answer: the second option
Explanation:
5) Question 5 Product
Answer: the fourth option:
which is the fourth option.
6) Question 6 Product
Answer: fourth option
Explanation:
which is the fourth option.
7) Question 7. Simplified form of 2√18 + 3√2 + √162
Answer: 18√2
Explanation:
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.