Question

Simplify (root 5 - root 3)2

Answer 1

(√5-√3)2

→ 2(√5-√3)

→ 2√5-2√3

If your question is (√5-√3)², this us the answer↓

→{√5²+√3²-2(√5)(√3)}

→5+3-2√15

→8-2√15

hope it helps…

Answer 2

Concept:

From the algebraic identities we know that, the square of difference between two numbers is equal to the difference between the sum of squares of that two numbers and the twice of the product of that numbers.

In mathematical word, $(a-b)^2=a^2+b^2-2ab$

The square of square root of a number gives back the number itself.

In mathematical word, $(\sqrt{A})^2=A$

Given:

Given the mathematical expression is $(\sqrt5-\sqrt3)^2$

Find:

The simplified value or form of the above given mathematical expression.

Solution:

Given mathematical expression is,

$(\sqrt5-\sqrt3)^2$

Using above mentioned algebraic identity in this problem we get,

$(\sqrt5-\sqrt3)^2=(\sqrt5)^2+(\sqrt3)^2-2\sqrt3\sqrt5=5+3-2\sqrt{15}=8-2\sqrt{15}$, this is an irrational number since $\sqrt{15}$ is an irrational and product of rational and irrational is irrational so $2\sqrt{15}$ is irrational and sum or difference between rational and irrational is also irrational so the number is irrational.

Hence the simplified form of the given mathematical expression $\mathbf{(\sqrt5-\sqrt3)^2=8-2\sqrt{15}}$.

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