Free Compass Math Practice Questions on Simplifying Expressions with Radicals with Solutions and Explanations - Sample 8

 Solutions with detailed explanations to compass math test practice questions in sample 8. 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 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 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 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) 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 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 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 2 √27 + 2 √75 = A) 16 √3 B) 4 √3 C) 4 √102 D) 16 E) 204 √(103) + √(105) = A) √10,100 B) 110 √10 C) 10,000 D) 2 √1000 E) 2 √100,000 Simplify the expression and rewrite it without radicals. √8 √3 √6 A) 144 B) 3 C) 17 D) 12 E) 4