Find the square root of the expression 55-14 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To find the square root of $55-14 \sqrt{6}$,we assume it is of the form $(a-b)^2 = a^2 + b^2 - 2ab$.We can rewrite the expression as $55 - 2 	ime

Vedclass · Accepted Answer

$7-\sqrt{6}$

Vedclass · Answer

(A) To find the square root of $55-14 \sqrt{6}$,we assume it is of the form $(a-b)^2 = a^2 + b^2 - 2ab$.We can rewrite the expression as $55 - 2 	imes 7 	imes \sqrt{6} 	imes \sqrt{1}$.Let $a = 7$ and $b = \sqrt{6}$.Then $a^2 + b^2 = 7^2 + (\sqrt{6})^2 = 49 + 6 = 55$.This matches the given expression.Therefore,$55 - 14 \sqrt{6} = 7^2 + (\sqrt{6})^2 - 2(7)(\sqrt{6}) = (7-\sqrt{6})^2$.The square root is $\sqrt{(7-\sqrt{6})^2} = 7-\sqrt{6}$.

Find the square root of the expression $55-14 \sqrt{6}$ in the form of a binomial surd.

Similar Questions

Prove that $\sqrt{2}+\sqrt{3}$ is irrational.

$A$ positive integer is of the form $3q + 1$,where $q$ is a natural number. Can you write its square in any form other than $3m + 1$,i.e.,$3m$ or $3m + 2$ for some integer $m$? Justify your answer.

Prove that the square of any odd positive integer is of the form $8m + 1$,where $m$ is a non-negative integer.

Show that the square of any positive integer cannot be of the form $5q+2$ or $5q+3$ for any integer $q$.

The following real number is expressed in decimal form. Determine whether it is rational or not. If rational,express it in the form of $\frac{p}{q}$. $5 . \overline{123456}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module