Question

1. which of the following is equal to square root (8x^9y^4
A. 3x^2y^2
B. 3x^4y^2 square root (2x
C. 9x^3y^2
D. 3x^3y^2 square root (2
2. what is the simplest form of the expression square root (2)- square root (10)/ square root (2)+square root (10)
A. -3/2+1/4 square root (10)
B. -3/2+1/2 square root (5)
C. 1-1/3 square root (5)
D. 1+1/2 square root (5)
3. what is the simplest form of the number 27^2/3
A. 3
B. 6
C. 9
D. 18

Answer 1

[square root (8x^9y^4)]²=8x^9y^4

[3x^4y^2 square root (2x)]²=9x^8y^4 .2x=18x^9y^4
the answer is
square root (18x^9y^4=
B. 3x^4y^2 square root (2x)




square root (2)- square root (10)/ square root (2)+square root (10)

(√2-√10) /√2+√10=(√2-√10) (√2-√10)/(√2+√10)(√2-√10 )=(√2-√10)²/2-10
2+10-2√5/-8=(√5-6)/4, it is the same of 
A. -3/2+1/4 square root (10)


27^2/3 =∛27²=∛3^3)^2=∛3^3x2=∛3^2)^3=3^2=9
 
the answer is
C. 9

Answer 2

The answer to each of the algebraic simplifications are;  3x⁴y²√(2x); -³/₂ + ¹/₄√10 and 9

How to simplify Algebra?

We want to find the square root of (8x^9y^4

= √((8x^9y^4)

Applying laws of exponents, we have the answer as;

⇒  3x⁴y²√(2x)

2) We want to find square root (2)- square root (10)/ square root (2)+square root (10). This is;

(√2 - √10)/(√2 + √10)

We rationalize the denominator by multiplying top and bottom by (√2 - √10) to get;

(√2 - √10)²/(2 - 10)

⇒ -³/₂ + ¹/₄√10

C) 27^(2/3) = (∛27)²

= 3² = 9

Read more about Algebra at; https://brainly.com/question/723406

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