Find the square root of - 19-8-3

The correct option is D 4+√(3) 19+8√(3) =16+3+2× 4 ×√(3) =(4+√(3))^2 .....................Using (a+b)^2=a^2+b^2+2ab ∴19+8√(3)=(4+ ...

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Byju's Answer

Standard IX

Mathematics

Relation between Square and Square Root

Find the squa...

Question

Find the square root of :
$19 + 8 \sqrt{3}$

14 + \sqrt{3}

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4 + \sqrt{2}

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4 + \sqrt{3}

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2 + \sqrt{3}

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Solution

The correct option is D $4 + \sqrt{3}$
$19 + 8 \sqrt{3}$

$= 16 + 3 + 2 \times 4 \times \sqrt{3}$

$= (4 + \sqrt{3})^{2}$ .....................Using $(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$∴ 19 + 8 \sqrt{3} = (4 + \sqrt{3})^{2}$

The square root of $(19 + 8 \sqrt{3})$ is $(4 + \sqrt{3})$

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Find the square root of :19+8√3

The correct option is D 4+√319+8√3=16+3+2×4×√3=(4+√3)2.....................Using (a+b)2=a2+b2+2ab∴19+8√3=(4+√3)2The square root of (19+8√3) is (4+√3)

Find the square root of :
$19 + 8 \sqrt{3}$

The correct option is D $4 + \sqrt{3}$
$19 + 8 \sqrt{3}$

$= 16 + 3 + 2 \times 4 \times \sqrt{3}$

$= (4 + \sqrt{3})^{2}$ .....................Using $(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$∴ 19 + 8 \sqrt{3} = (4 + \sqrt{3})^{2}$

The square root of $(19 + 8 \sqrt{3})$ is $(4 + \sqrt{3})$