Question

if a=7-4√3 find the value of √a+1\√a

Answer 1

• a=7-2root 12
• root a=2-root 3
• 1/root a=2+root3
• by this root a+1/root a =
• 2+root3 +2-root3
• 4 is the answer

Answer 2

Solution :-

Finding the value of √a

a = 7 - 4√3

⇒ a = 7 - 2(2)(√3)

⇒ a = 4 + 3 - 2(2)(√3)

⇒ a = 2² + (√3)² - 2(2)(√3)

⇒ a = (2 - √3)²

Since a² + b² - 2ab = (a - b)²

Taking square root on both sides

⇒ √a = √(2 - √3)²

⇒ √a = 2 - √3

Finding 1/√a

1/√a = 1/(2 - √3)

Rationalise the denominator

= 1/(2 - √3) * (2 + √3)/(2 + √3)

= {2 + √3}/{2² - (√3)²}

= (2 + √3)/(4 - 3)

= (2 + √3)/1

1/√a = 2 + √3

Findind √a + 1/√a

√a + 1/√a

= 2 - √3 + (2 + √3)

= 2 - √3 + 2 + √3

= 4

Therefore the value of √a + 1/√a is 4