Find the square root of the expression 56-24 | vedclass

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(D) To find the square root of $56-24 \sqrt{5}$,we assume it is of the form $(a-b\sqrt{c})^2 = a^2 + b^2c - 2ab\sqrt{c}$.Comparing $56-24\sqrt{5}$ wit

Vedclass · Accepted Answer

$6-2 \sqrt{5}$

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(D) To find the square root of $56-24 \sqrt{5}$,we assume it is of the form $(a-b\sqrt{c})^2 = a^2 + b^2c - 2ab\sqrt{c}$.Comparing $56-24\sqrt{5}$ with $a^2+b^2c - 2ab\sqrt{c}$,we have $2ab\sqrt{c} = 24\sqrt{5}$.Let $a=6$ and $b\sqrt{c} = 2\sqrt{5}$.Then $a^2 + b^2c = 6^2 + (2\sqrt{5})^2 = 36 + 20 = 56$.This matches the given expression.Therefore,$\sqrt{56-24\sqrt{5}} = 6-2\sqrt{5}$.

Find the square root of the expression $56-24 \sqrt{5}$ in the form of a binomial surd.

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