Rationalize the denominator of 16/root 45-5
Answers
Answer:
So, in order to rationalize the denominator, we need to get rid of all radicals that are in the denominator.
Step 1: Multiply numerator and denominatorby a radical that will get rid of the radical in the denominator. ...
Step 2: Make sure all radicals are simplified. ...
Step 3: Simplify the fraction if needed.
Answer:
41
−5
16
=(
41
+5)
Step-by-step explanation:
Given: \frac{16}{\sqrt{41}-5}
41
−5
16
WE have to rationalize the denominator.
Consider the given fraction \frac{16}{\sqrt{41}-5}
41
−5
16
Multiply and divide by (\sqrt{41}+5)(
41
+5) , we get,
\frac{16}{\sqrt{41}-5}\times \frac{\sqrt{41}+5}{\sqrt{41}+5}
41
−5
16
×
41
+5
41
+5
Thus,
Denominator becomes (a+b)(a-b)=a^2-b^2(a+b)(a−b)=a
2
−b
2
We have,
(\sqrt{41}+5)(\sqrt{41}-5)=(\sqrt{41})^2-5^2=41-25=16(
41
+5)(
41
−5)=(
41
)
2
−5
2
=41−25=16
Thus, \frac{16}{\sqrt{41}-5}\times \frac{\sqrt{41}+5}{\sqrt{41}+5}=\frac{16(\sqrt{41}+5)}{16}=(\sqrt{41}+5)
41
−5
16
×
41
+5
41
+5
=
16
16(
41
+5)
=(
41
+5)
Thus, \frac{16}{\sqrt{41}-5}=(\sqrt{41}+5)
41
−5
16
=(
41 +5)