Question

rationalize root 5 + root 2 upon root 5 minus root 2​

Answer 1

Answer:

thanl u

Step-by-step explanation:

donevhdhdhdhhdhdd

Answer 2

Concept:

Rationalization:  Rationalization is the process or method of eliminating irrational numbers from the denominator.

Given:

root 5 + root 2 upon root 5  - root 2

(√5 + √2)/(√5 - √2)

Find:

Rationalize the given number.

Answer:

(√5 + √2)/(√5 - √2) =  $\frac{(7 + 2\sqrt{10}) }{3}$

Solution:

Given that, (√5 + √2)/(√5 - √2)

To rationalize it, we will multiply and divide it by (√5 + √2).

(√5 + √2)/(√5 - √2) = [(√5 + √2)/(√5 - √2)] × [(√5 + √2)/(√5 + √2)]

                                 = [(√5 + √2)×(√5 + √2)]/[(√5 - √2)×(√5 + √2)]

                                 =  $\frac{(\sqrt{5}+\sqrt{2})(\sqrt{5}+\sqrt{2}) }{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}$

                                 = (√5 + √2)²/(√5)² - (√2)²

                                 = [(√5)² + (√2)² + 2√5√2] / (5 - 2)

                                 = (5 + 2 + 2√10) / 3

                                 = ( 7 + 2√10)/3

                                 = 7/3 + 2√10/3

                                = $\frac{7}{3} + \frac{2\sqrt{10} }{3}$ or $\frac{(7 + 2\sqrt{10}) }{3}$

Hence, after rationalizing it we get  $\frac{(7 + 2\sqrt{10}) }{3}$.

#SPJ2