Question

simplify by rationalising the denominator root 7 upon 9 + 2 root 5​

Answer 1

Answer

$\frac{9\sqrt{7}-2\sqrt{35} }{61 }$

Step-by-step explanation:

Rationalize the denominator of $\frac{ \sqrt{7} }{9+2\sqrt{5} }$ by multiplying numerator and denominator by $9-2\sqrt{5}$ .

• $\frac{\sqrt{7 }(9-2\sqrt{5}) }{(9+2\sqrt{5} )(9-2\sqrt{5}) }$

Consider $(9+2\sqrt{5})(9-2\sqrt{5} )$. Multiplication can be transformed into difference of squares using the rule: $(a-b)(a+b)=a^{2} - b^{2}$

• $\frac{\sqrt{7}(9-2\sqrt{5}) }{9^{2} - (2\sqrt{5})^{2} }$

Calculate 9 to the power of 2 and get 81.

• $\frac{\sqrt{7}(9-2\sqrt{5}) }{81- (2\sqrt{5})^{2} }$

Expand $(2\sqrt{5})^{2}$

• $\frac{\sqrt{7}(9-2\sqrt{5}) }{81- 2^{2} (\sqrt{5})^{2} }$

Calculate 2 to the power of 2 and get 4.

• $\frac{\sqrt{7}(9-2\sqrt{5}) }{81- 4 (\sqrt{5})^{2} }$

The square of $\sqrt{5}$ is 5.

• $\frac{\sqrt{7}(9-2\sqrt{5}) }{81- 4 * 5 }$

Multiply 4 and 5 to get 20.

• $\frac{\sqrt{7}(9-2\sqrt{5}) }{81- 20 }$

Subtract 20 from 81 to get 61.

• $\frac{\sqrt{7}(9-2\sqrt{5}) }{61 }$

Use the distributive property to multiply $\sqrt{7}$ by $9-2\sqrt{5}$ .

• $\frac{9\sqrt{7}-2\sqrt{7} \sqrt{5} }{61 }$

To multiply $\sqrt{7}$ and $\sqrt{5}$,multiply the numbers under the square root.

• $\frac{9\sqrt{7}-2\sqrt{35} }{61 }$

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Answer 2

Step-by-step explanation:

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