rationalise the denominator 1 / root 3 + root 2
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Step-by-step explanation:
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Step-by-step explanation:
Given:
1/(√3 + √2)
To find:
Rationalising the denominator
Solution:
1(√3 + √2)
The denominator is √3 + √2
We know that
Rationalising factor of √a + √b = √a - √b.
Therefore, the rationalising factor of √3 + √2 = √3 - √2.
On rationalising the denominator them
→ [1/(3 + √2)] × [(√3 - √2)/(√3 - √2)]
→ [1(√3 - √2)]/[(√3 + √2)(√3 - √2)]
since, (a+b)(a-b) = a^2 - b^2
where, a = √3
and b = √2.
→ [1(√3 - √2)]/[(√3)^2 - (√2)^2]
→ [1(√3 - √2)]/(3 - 2)
→ [1(√3 - √2)]/1
→ 1(√3 - √2)
→ √3 - √2 Ans .
Hence, the denominator is rationalised.
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