Find the value of 3-53-5-

The correct option is C 4We know the identity: a^2 b^2 = (a+b)(a b) (3+√(5))(3 √(5)) =(3^2 (√(5))^2 nbsp;=9 5=4 nbsp; Hence, (3+√(5))(3 √(5))= 4, wh ...

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Byju's Answer

Standard IX

Mathematics

Operations on Rational and Irrational Numbers

Find the valu...

Question

Find the value of $(3 + \sqrt{5}) (3 - \sqrt{5})$ .

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Solution

The correct option is D 4
We know the identity:
$a^{2} - b^{2} = (a + b) (a - b)$

$(3 + \sqrt{5}) (3 - \sqrt{5}) = (3^{2} - (\sqrt{5})^{2} = 9 - 5 = 4$

Hence, $(3 + \sqrt{5}) (3 - \sqrt{5}) = 4$ , which is a rational number.

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Similar questions

Q. Value of

(3 + \sqrt{5}) (3 - \sqrt{5})

is .

Q. If

p = \frac{3 - \sqrt{5}}{3 + \sqrt{5}} and q = \frac{3 + \sqrt{5}}{3 - \sqrt{5}}

, find the value of p² + q².

Q. Find the value of

{(\frac{3^{0} \times 5^{3} \times 5^{- 3}}{3^{- 1}})}^{- 1}

Q. The value of

{(3 \sqrt{5})}^{3}

a \sqrt{5}

then find

a

Q. Find the value of x for which

{(\frac{5}{3})}^{- 4} \times {(\frac{5}{3})}^{- 5} = {(\frac{5}{3})}^{3 x} .

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Find the value of (3+√5)(3−√5) .

The correct option is D 4We know the identity: a2−b2=(a+b)(a−b) (3+√5)(3−√5)=(32−(√5)2=9−5=4 Hence, (3+√5)(3−√5)=4, which is a rational number.

Find the value of $(3 + \sqrt{5}) (3 - \sqrt{5})$ .

The correct option is D 4
We know the identity:
$a^{2} - b^{2} = (a + b) (a - b)$

$(3 + \sqrt{5}) (3 - \sqrt{5}) = (3^{2} - (\sqrt{5})^{2} = 9 - 5 = 4$

Hence, $(3 + \sqrt{5}) (3 - \sqrt{5}) = 4$ , which is a rational number.