(√10 - √5)/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 (√10 - √5)/2
We have to rationalise the denominator and evaluate the given expression.
√10 = √5 × √2
So, (√10 - √5) = (√5 × √2) - √5
Taking out common term,
= √5(√2 - 1)
Given, √5 = 2.236
√2 = 1.414
So, √5(√2 - 1) = 2.236(1.414 - 1)
= 2.236(0.414)
= 0.9257
Now, (√10 - √5)/2 = 0.9257/2
= 0.4628
Therefore, (√10 - √5)/2 = 0.463
✦ 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 √12/2
Given, the expression is √12/2
We have to rationalise the denominator and evaluate the given expression.
√12 = √4 × √3 = 2√3
So, √12/2 = 2√3/2
= √3
Given, √3 = 1.732
Therefore, √12/2 = 1.732
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 13(iii)
(√10 - √5)/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 (√10 - √5)/2 by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236, we get 0.463
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