Question

If √2 = 1.4 and √3 = 1.7, find the value of 1/(√3 – √2)

Answer 1

If √2 = 1.4 and √3 = 1.7, the value of 1/(√3 – √2) is 3.1 .

• Given,

√2 = 1.4, and √3 = 1.7

• Therefore,

1 / (√3 - √2) = (√3 + √2) / { (√3 - √2) (√3 + √2) }  

[ • Here, the denominator is an irrational number. So, it has to be first converted into a rational number.

• For doing so, the denominator is multiplied with itself by inversing the sign in between.

• Since the denominator is multiplied by (√3 + √2), the numerator must also be multiplied by the same term in order to keep the original expression unchanged.]

Or, 1 / (√3 – √2)  = (√3 + √2) / {(√3)² - (√2)² }

[ Applying a² - b² = (a - b) (a + b) in the denominator ]

Or, 1 / (√3 – √2) = (√3 + √2) / (3 - 2)

Or, 1 / (√3 – √2) = (√3 + √2) / 1

Or, 1 / (√3 – √2) = (√3 + √2)

Now, putting the values of √3 and √2, we get,

1 / (√3 – √2) = 1.7 + 1.4 = 3.1

Therefore, 1 / (√3 - √2) = 3.1

Answer 2

1/(√3 – √2) = 3.1

Explanation:

Given, √2 = 1.4, and √3 = 1.7

1 / (√3 - √2)

Multiplying both numerator and denominator with (√3 + √2), we get:

1 / (√3 - √2) = (√3 + √2) / { (√3 - √2) (√3 + √2) }  

 = (√3 + √2) / {(√3)² - (√2)² }

= (√3 + √2) / (3 - 2)

= (√3 + √2) / 1

So we get 1 / (√3 – √2) = √3 + √2

Substituting the given values, we get:

1 / (√3 – √2) = √3 + √2 = 1.7 + 1.4 = 3.1