Question

Given that √2 = 1.414, √3 = 1.732, √5 = 2.236 and √7 = 2.646 find the square roots of the following:

(i) 196/75

(ii) 400/63

(iii) 150/7

Answer 1

(i) 196/75

√(196/75) = √(196)/ √ (75)

= √(14×14)/ √(5×5×3)

= 14/ (5√3)

= 14/ (5×1.732)

= 14/8.66

= 1.617

(ii) 400/63

√(400/63) = √(400)/ √ (63)

= √(20×20)/ √(3×3×7)

= 20/ (3√7)

= 20/ (3×2.646)

= 20/7.938

= 2.520

(iii) 150/7

√(150/7) = √(150)/ √ (7)

= √(3×5×5×2)/ √ (7)

= (5√3×√2)/ (√7)

= 5×1.732×1.414/ (2.646)

= 12.245/2.646

= 4.628