rationalise : 30/5 root3 + 3 root5
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Secondary School Math 50 points
Rationalise this
30/5√3-3√5=
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THE BRAINLIEST ANSWER!
HarishAS
Hey friend, Harish here.
Here is your answer:
To rationalize the expression:
\frac{30}{5 \sqrt{3} -3 \sqrt{5} }
Solution:
To rationalize a number we must multiply and divide the number by it's conjugate.
Conjugate of denominator is 5√3 + 3√5.
Then,
\frac{30}{5 \sqrt{3} -3 \sqrt{5} }= \frac{30}{5 \sqrt{3} -3 \sqrt{5} }\times \frac{5 \sqrt{3} +3 \sqrt{5}}{5 \sqrt{3} +3 \sqrt{5}}
We know that,
( a+b)(a-b) =a^{2}-b^{2}
Using the identity to multiply the denominators , We get.
(5 \sqrt{3} -3 \sqrt{5})(5 \sqrt{3} +3 \sqrt{5}) = (5 \sqrt{3})^{2} -(3 \sqrt{5})^{2} = 75 -45 = 30
Then,
\frac{30}{5 \sqrt{3} -3 \sqrt{5} }\times \frac{5 \sqrt{3} +3 \sqrt{5}}{5 \sqrt{3} +3 \sqrt{5}} = \frac{(30)(5 \sqrt{3} +3 \sqrt{5}) }{30} = \frac{5 \sqrt{3} -3 \sqrt{5} }{1} =5 \sqrt{3} -3 \sqrt{5}