Question

simplify 1 upon 3 + under root 5

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Answer 1

Answer:

$\frac{3 - \sqrt{5} }{4}$ is the required value of $\frac{1}{3 + \sqrt{5} }$.

Step-by-step explanation:

Explanation:

Given, that 1 upon3 + under root 5

This can be written as,  $\frac{1}{3 + \sqrt{5} }$

To simplify this numerical, we need to first rationalize its denominator.

To rationalize the denominator:

• Therefore, we must remove all radicals from the denominator to justify it.

• Remove the radical from the denominator by multiplying the numerator and denominator by the same radical.

• Ensure that all radicals are condensed.

• If necessary, simplify the fraction.

Step 1:

By multiplying numerator and denominator by $3 - \sqrt{5}$ we get,

⇒$\frac{1}{3 + \sqrt{5} }$ × $\frac{3 - \sqrt{5} }{3 - \sqrt{5} }$ = $\frac{3 - \sqrt{5} }{3^2 - (\sqrt{5} )^2}$

⇒$\frac{3 - \sqrt{5} }{9 - 5}$ = $\frac{3 - \sqrt{5} }{4}$

Final answer:

Hence, $\frac{3 - \sqrt{5} }{4}$ this is the required answer.

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Answer 2

Correct Question

Simplify

$\frac{1}{3+\sqrt5}$

Answer:

simplifying the given fraction we get

$=\frac{3-\sqrt5}{4}$

Step-by-step explanation:

Given :

Since we are given the expression

$\frac{1}{3+\sqrt5}$

To Find :

Simplify the given expression by rationalizing  

Solution :

Since we are given the expression to rationalize is

= $\frac{1}{3+\sqrt{5}}$

Rationalizing Steps :

• First multiply by the conjugate of denominator in the numerator and denominator both.
• Apply suitable identity to simplify the denominator.

$=\frac{1}{3+\sqrt5}$

multiply by the conjugate of denominator in the numerator and denominator both.

$=\frac{1}{3+\sqrt5}\ \text{x} \ \frac{3-\sqrt5}{3-\sqrt5}$

$= \frac{3-\sqrt5}{3^2-(\sqrt5)^2}$

since we know that $(a+b)(a-b)=a^2-b^2$

simplifying

$=\frac{3-\sqrt5}{9-4} = \frac{3-\sqrt5}{4}$

$= \frac{3-\sqrt5}{4}$

Hence simplifying given expression by rationalizing we get

$\frac{3-\sqrt5}{4}$

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