Solutions with detailed explanations to compass math test practice questions in sample 8.
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Simplify the expression with radicals given below
2 √50 + 12 √8
Solution
Use the fact that 50 = 2*25 and 8 = 2*4 to write
2 √50 + 12 √8
= 2 √(2*25) + 12 √(2*4)
= 2 √2 √25 + 12 √2 √4
Simplify
= 2 * 5 * √2 + 12 * 2 * √2
= 10 √2 + 24 √2 = 34 √2
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Simplify the expression given below
√27 - √300
Solution
Use the fact that 27 = 3*9 and 8 = 3*100 to write
√27 - √300
= √(3*9) - √(3*100)
= √3 √9 - √3 √100
Simplify
= 3 √3 - 10 √3 = - 7 √3
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Simplify the expression with radicals given below
- 2 √(16y) + 10 √y
Solution
We first write
- 2 √(16y) + 10 √y
= - 2 √16 √y + 10 √y
simplify
= - 2 * 4 √y + 10 √y
= -8 √y + 10 √y
= 2 √y
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Simplify the expression given below
2 √(x + 1) + 3 √(16x + 16)
Solution
We first factor (16x + 16) under the radical
2 √(x + 1) + 3 √(16x + 16)
= 2 √(x + 1) + 3 √[ 16(x + 1) ]
= 2 √(x + 1) + 3 √16 √(x + 1)
Simplify
= 2 √(x + 1) + 3 * 4 * √(x + 1)
= 2 √(x + 1) + 12 √(x + 1)
= 14 √(x + 1)
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2 √3 + 4 √12 + 3 √48 =
Solution
We first rewrite the given expression as
2 √3 + 4 √12 + 3 √48
= 2 √3 + 4 √(3*4) + 3 √(3*16)
= 2 √3 + 4 √3 √4 + 3 √3 √16
Simplify
= 2 √3 + 8 √3 + 12 √3
= 22 √3
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Simplify the expression given below and rewrite it without radicals
(√3 + √12) / (√3 - √12)
Solution
We first rewrite the given expression as
(√3 + √12) / (√3 - √12)
= (√3 + √(3*4) / (√3 - √(3*4))
Simplify
= (√3 + 2 √3 / (√3 - 2 √3)
= 3√3 / - √3
= - 3
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Simplify the expression with radicals given below
5 √x + 6 √(9x) - 10 √(16x)
Solution
We first rewrite the given expression as
5 √x + 6 √(9x) - 10 √(16x)
= 5 √x + 6 √9 √x - 10 √16 √x
Simplify
= 5 √x + 6*3 √x - 10*4 √x
= 5 √x + 18 √x - 40 √x
= -17 √x
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2 √27 + 2 √75 =
A) 16 √3
B) 4 √3
C) 4 √102
D) 16
E) 204
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√(103) + √(105) =
A) √10,100
B) 110 √10
C) 10,000
D) 2 √1000
E) 2 √100,000
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Simplify the expression and rewrite it without radicals.
√8 √3 √6
A) 144
B) 3
C) 17
D) 12
E) 4
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