Question

rationalizing factor of 5√3 is with explanation​

Answer 1

question ⤵️

hi mate I think you question should be

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

Answer ⤵️

$\frac{1}{5 \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \frac{ \sqrt{3} }{15}$

consept used here

the rationalization of surds. When the denominator of an expression is a surd which can be reduced to an expression with rational denominator, this process is known as rationalizing the denominator of the surd.

the rationalization of surds. When the denominator of an expression is a surd which can be reduced to an expression with rational denominator, this process is known as rationalizing the denominator of the surd.If a surd or surd with rational numbers present in the denominator of an equation, to simplify it or to omit the surds from the denominator, rationalization of surds is used. Surds are irrational numbers but if multiply a surd with a suitable factor, result of multiplication will be rational number. This is the basic principle involved in rationalization of surds. The factor of multiplication by which rationalization is done, is called as rationalizing factor. If the product of two surds is a rational number, then each surd is a rationalizing factor to other. Like if 2–√ is multiplied with 2–√, it will 2, which is rational number, so 2–√ is rationalizing factor of 2–√.

the rationalization of surds. When the denominator of an expression is a surd which can be reduced to an expression with rational denominator, this process is known as rationalizing the denominator of the surd.If a surd or surd with rational numbers present in the denominator of an equation, to simplify it or to omit the surds from the denominator, rationalization of surds is used. Surds are irrational numbers but if multiply a surd with a suitable factor, result of multiplication will be rational number. This is the basic principle involved in rationalization of surds. The factor of multiplication by which rationalization is done, is called as rationalizing factor. If the product of two surds is a rational number, then each surd is a rationalizing factor to other. Like if 2–√ is multiplied with 2–√, it will 2, which is rational number, so 2–√ is rationalizing factor of 2–√.In other words, the process of reducing a given surd to a rational form after multiplying it by a suitable surd is known as rationalization.

Answer 2

Rationalizing factor of 5√3 is √3.

Given:

An irrational number 5√3.

To Find:

Rationalizing factor of 5√3.

Solution:

Rationalizing factor is the factor with which both numerator and denominator must be multiplied in order to get denominator rationalized.

5√3 can also be written as;

(5√3 x √3)/ (√3)

=> 15/√3

Now, we have √3 at denominator.

Hence, the rationalizing factor = $3^{(1-1/2)}$

=√3

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