1/(√3 + √2). Rationalise the denominator and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236, upto three places of decimal
Solution:
Given, the expression is 1/(√3+√2)
We have to rationalise the denominator and evaluate the given expression.
To rationalise we have to take conjugate,
1/(√3+√2) = 1/(√3+√2) × (√3-√2)/(√3-√2)
= (√3-√2) / (√3+√2)(√3-√2)
By using algebraic identity,
(a² - b²) = (a - b)(a + b)
(√3-√2)(√3+√2) = (√3)² - (√2)²
= 3 - 2
= 1
So, (√3-√2) / (√3+√2)(√3-√2) = (√3-√2)/(1)
= (√3-√2)
Given, √2 = 1.414
√3 = 1.732
So, √3-√2 = 1.732 - 1.414
= 0.318
Therefore, 1/(√3+√2) = 0.318
✦ Try This: Rationalise the denominator of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236, upto three places of decimal √5/(√3+√5)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 13(v)
1/(√3 + √2). Rationalise the denominator and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236, upto three places of decimal
Summary:
On rationalising the denominator and evaluating the expression 1/(√3+√2) by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236, we get 0.318
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