Question

Rationalize the denominator of the fraction below. What is the new
denominator?
4/3+√7​

Answer 1

Answer:

The new denominator is 2

Answer 2

The new denominator of the fraction after rationalization is 2.

What is a rational number?

A rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0. It can be made by dividing an integer by an integer.

For the given situation,

The rational number is 4/(3+√7)

The denominator of the fraction can be rationalize as

$\frac{4}{3+\sqrt{7} }=\frac{4}{3+\sqrt{7} } (\frac{3-\sqrt{7} }{3-\sqrt{7} } )$

⇒ $\frac{4}{3+\sqrt{7} }=\frac{4(3-\sqrt{7})}{(3+\sqrt{7} )(3-\sqrt{7})}$            [∵ (a+b)(a-b) = a²-b²]

⇒ $\frac{4}{3+\sqrt{7} }=\frac{4(3-\sqrt{7})}{3^{2} -(\sqrt{7})^{2} }$

⇒ $\frac{4}{3+\sqrt{7} }=\frac{4(3-\sqrt{7})}{9-7}$

⇒ $\frac{4}{3+\sqrt{7} }=\frac{4(3-\sqrt{7})}{2}$

Hence we can conclude that the new denominator of the fraction after rationalization is 2.

Learn more about rational numbers here    

https://brainly.com/question/13261309

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