Find the square root of 30-2 sqrt{56}. | vedclass

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

Question

(C) To find the square root of $30-2 \sqrt{56}$,we express it in the form $(a-b)^2 = a^2+b^2-2ab$.We need to find two numbers such that their sum of s

Vedclass · Accepted Answer

$2 \sqrt{7}-\sqrt{2}$

Vedclass · Answer

(C) To find the square root of $30-2 \sqrt{56}$,we express it in the form $(a-b)^2 = a^2+b^2-2ab$.We need to find two numbers such that their sum of squares is $30$ and their product is $\sqrt{56}$.$30-2 \sqrt{56} = 30-2 \sqrt{28 	imes 2} = 30-2 \sqrt{7 	imes 8}$.We can write $30$ as $(28+2)$ or $(7+23)$,but looking at the factors of $56$,we have $56 = 28 	imes 2$ or $7 	imes 8$.Let the expression be $(\sqrt{x}-\sqrt{y})^2 = x+y-2 \sqrt{xy}$.Here,$x+y = 30$ and $xy = 56$.Solving for $x$ and $y$,we find $x=28$ and $y=2$.Thus,$30-2 \sqrt{56} = 28+2-2 \sqrt{28 	imes 2} = (\sqrt{28}-\sqrt{2})^2$.Since $\sqrt{28} = \sqrt{4 	imes 7} = 2 \sqrt{7}$,the expression becomes $(2 \sqrt{7}-\sqrt{2})^2$.Therefore,the square root is $2 \sqrt{7}-\sqrt{2}$.

Find the square root of $30-2 \sqrt{56}$.

Similar Questions

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{15}{1600}$

The length,breadth,and height of a prayer room are $15\,m$,$12\,m$,and $21\,m$ respectively. Determine the longest rod which can measure the three dimensions of the room exactly. (in $,m$)

The decimal form of $\frac{12}{35}$ is $\ldots \ldots \ldots \ldots$

By using the fact $g.c.d. (a, b) \times l.c.m. (a, b) = a \times b$,find $l.c.m. (26, 91)$.

Find : $\sqrt{7+2 \sqrt{10}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module