How do you simplify #1/sqrt7#?

Answer 1

All you can do is rationalize the denominator.

To rationalize the denominator just means to make the denominator a rational number. We can do this by multiplying the numerator and the denominator by #sqrt(7)#, in order to keep the expression equivalent.
#1/sqrt(7) xx sqrt(7)/sqrt(7)#
#= sqrt(7)/sqrt(49)#
#= sqrt(7)/7#

This is as far as we can simplify. Here are the two rules about rationalizing a denominator:

When a monomial (one term in the denominator): Multiply the numerator and the denominator by the radical in the original expression's denominator

When a binomial (two terms in the denominator): Multiply the numerator and the denominator by the conjugate of the radical in the original expression. The conjugate forms a difference of squares. Example: #sqrt(2) + 4# is the conjugate of #sqrt(2) - 4#. Essentially, you must switch the sign in the middle.

Practice exercises:

a) #4/sqrt(5)#
b) #(3 + sqrt(6))/sqrt(2)#
c) #(5 - sqrt(7))/(sqrt(10) - sqrt(11))#
d) #(sqrt(3) + sqrt(2))/(5 + sqrt(6))#
  1. Challenge question:
Rationalise the denominator of #sqrt(2)/sqrt((x^2 + 6x + 5))#
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Answer 2

To simplify 1/sqrt(7), you can multiply both the numerator and denominator by sqrt(7). This results in sqrt(7)/7.

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Answer 3

To simplify ( \frac{1}{\sqrt{7}} ), you can rationalize the denominator by multiplying the numerator and denominator by ( \sqrt{7} ):

[ \frac{1}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{7}}{7} ]

Therefore, ( \frac{1}{\sqrt{7}} ) simplifies to ( \frac{\sqrt{7}}{7} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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