Question

If x² = 500 (x > 0) , then find √20 + √45 + √125 = ?


answer: x

Answer 1

Given :

• x² = 500
• (x > 0)

To find :

• √20 + √45 + √125

Solution :

• x²= 500
• x = √500
• x = √100 × 5
• x = 10√5

☯ Value of x : 10√5

• √20 + √45 + √125
• √4×5 + √9×5 +√25×5
• 2√5 + 3√5 + 5√5
• 2² = 4   3² = 9   5² = 25
• Roots are same : √5 (So add)
• 2 + 3 + 5 = 10
• 10√5

☯ We know, x is 10√5

☯ Hence, the value of √20 + √45 + √125 if x² = 500 is x

Answer 2

x²= 500

x = √500

x = √100 × 5

x = 10√5

☯ Value of x : 10√5

√20 + √45 + √125

√4×5 + √9×5 +√25×5

2√5 + 3√5 + 5√5

2² = 4   3² = 9   5² = 25

Roots are same : √5 (So add)

2 + 3 + 5 = 10

10√5