Question

rationalise the denominator of following: 1/3+√2
$1 \div 3 + \sqrt{2}$


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Answer 1

Answer:

Numerator is 1. But the denominator is 3+√2 which is an irrational number. ... The rationalising factor or conjugate surd of 3+√2 is 3-√2. =>Which means we have to multiply the numerator and denominator by 3-√2 to rationalise the denominator of this number

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Answer 2

Given :

• 1 / 3 + √2

To Find :

• Rationalise the denominator .

Solution :

$\longmapsto\tt{\dfrac{1}{3+\sqrt{2}}}$

$\longmapsto\tt{\dfrac{1}{3+\sqrt{2}}\times\dfrac{3-\sqrt{2}}{3-\sqrt{2}}}$

Using Identity = (x + y) (x - y) = x² - y² :

$\longmapsto\tt{\dfrac{3-\sqrt{2}}{{(3)}^{2}-{(\sqrt{2})}^{2}}}$

$\longmapsto\tt{\dfrac{3-\sqrt{2}}{9-2}}$

$\longmapsto\tt\bf{\dfrac{3-\sqrt{2}}{7}}$

So , The Final answer is 3 - √2 / 7 ..

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Some More Identities :

• (x + y)² = x² + 2xy + y²
• (x - y)² = x² - 2xy + y²
• x² - y² = (x + y) (x - y)
• (x + a) (x + b) = x² + (a + b)x + ab
• (x + y + z) = x² + y² + z² + 2xy + 2yz +2zx
• (x + y)³ = x³ + y³ + 3xy (x+y)
• (x - y)³ = x³ - y³ - 3xy (x-y)

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