According to the identity, (√(a)+√(b)) ^2 = a+b+2√a nbsp;×√b so, we can write the given expression as: (√(6)+√(3)) ^2 = 6+3+2√6×√3 nbsp; nbsp; nbsp; ...

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Byju's Answer

Standard IX

Mathematics

Rationalising Surds

Solve √6+√3 2

Question

Solve ( $\sqrt{6}$ + $\sqrt{3})^{2}$

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Solution

According to the identity,
( $\sqrt{a}$ + $\sqrt{b})^{2}$ = a+b+2√a ×√b
so, we can write the given expression as:
( $\sqrt{6}$ + $\sqrt{3})^{2}$ = 6+3+2√6×√3
= 9+2√18
= 9+2×3√2
= 9+6√2

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Solve (√6+√3)2

According to the identity, (√a+√b)2 = a+b+2√a ×√b so, we can write the given expression as: (√6+√3)2 = 6+3+2√6×√3 = 9+2√18 = 9+2×3√2 = 9+6√2

Solve ( $\sqrt{6}$ + $\sqrt{3})^{2}$

According to the identity,
( $\sqrt{a}$ + $\sqrt{b})^{2}$ = a+b+2√a ×√b
so, we can write the given expression as:
( $\sqrt{6}$ + $\sqrt{3})^{2}$ = 6+3+2√6×√3
= 9+2√18
= 9+2×3√2
= 9+6√2