Question

rationalise the denominator 3+√2/4√2

Answer 1

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3+root 2/4root2

=3+root 2/4root2*4root2/4root2

=(3+root 2*4root2)/32

=12root2+8/32

=4(3root2+2)/32

=3root2+2/8

Answer 2

Question

Rationalise the denominator → $\dfrac{3+ \sqrt{2}}{4\sqrt{2} }$

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Answer

The rationalizing factor for the denominator for this question would be √2. So we would multiply the numerator and denominator by √2.

$\sf \implies \dfrac{3+ \sqrt{2}}{4\sqrt{2} }\times \dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf \implies \dfrac{\sqrt{2} (3+ \sqrt{2})}{4\sqrt{2} \times \sqrt{2}}$

$\sf \implies \dfrac{\sqrt{2} (3)+ \sqrt{2(} \sqrt{2})}{4\times \sqrt{2} \times \sqrt{2}}$

$\sf \implies \dfrac{3\sqrt{2} + {2}}{4\times 2}$

$\sf \implies \dfrac{3\sqrt{2} + {2}}{8}$

∴ Upon rationalizing the denominator of $\bf \dfrac{3+ \sqrt{2}}{4\sqrt{2} }$ we get $\bf \dfrac{3\sqrt{2} + {2}}{8}$.

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Additional Information

• When we square a root of the same number, we get the same number simplified without root. Let's understand this with an example -:

(√2)² = √2 × √2 = 2

∴ (√2)² = 2

• Conjugate → Expression obtained upon changing the middle sign of the ideal expression. For example ⇒

Conjugate of √2 - 3 would be √2 + 3

• Rationalizing factor is a factor which when multiplied with the numerator or denominator of an irrational number gives a rational number (only in the numerator or denominator part of the number)

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