Question

How do you find the value of (√2 + 1) / √5 given that √2= 1.414, √10 = 3.162 & √5 = 2.236?step by step explanation in note​

Answer 1

Step-by-step explanation:

Given :-

√2= 1.414,

√10 = 3.162

√5 = 2.236

To find :-

Find the value of (√2+1)/√5 ?

Solution :-

Method -1:-

Given that :-

(√2+1)/√5

The denominator = √5

The Rationalising factor of√5 = √5

On Rationalising the denominator then

=>[(√2+1)/√5)]×(√5/√5)

=> (√2+1)√5)/(√5×√5)

=> (√2+1)√5/ (√5)²

=> [(√2×√5)+(1×√5)] / 5

=>(√10+√5)/5

On Substituting the values of √10 and √5

=> (3.162+2.236) / 5

=> 5.398 / 5

=> 1.0796

Method -2:-

Given that :-

(√2+1)/√5

On Substituting the value of √2 and √5

=> (1.414+1)/(2.236)

=> 2.414/2.236

=> (2414/1000)/(2236/1000)

=> 2414/2236

=> 1207/1118

=> 1.0796

Answer:-

The value of (√2+1)/√5 for the given problem is 1.0796

Used Method :-

• Rationalising the denominator.

Points to know :-

• The product of two irrational numbers is a rational number then they are called Rationalising factors to each other.

• Every number has so many Rationalising factors

• Rationalising factor of √a = √a

Used values :-

• √2= 1.414,
• √10 = 3.162

• √5 = 2.236

Answer 2

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