Question

CAN SOMEONE PLEASE ANSWER THIS SOON! THANK YOU!
What is one-half of the reciprocal of 7/sqrt(98)? Express your answer in the form sqrt(a)/b where sqrt(a) is in simplest radical form.

Answer 1

We want to find one-half of the reciprocal of 7/sqrt(98). Let's write down an expression for this:

$\dfrac{1}{2} \times \dfrac{\sqrt{98}}{7}$

We can rewrite 98 into $2 \times 49$

$\dfrac{1}{2} \times \dfrac{\sqrt{2 \times 49}}{7}$

$=\dfrac{1}{2} \times \dfrac{\sqrt{2} \times \sqrt{49}}{7}$

The square root of 49 is 7

$=\dfrac{1}{2} \times \dfrac{\sqrt{2} \times 7}{7}$

$=\dfrac{1}{2} \times\sqrt{2}$

$=\dfrac{\sqrt{2}}{2}$

This should be your answer. Let me know if you need any clarifications, thanks!

Answer 2

Answer:

√2/2

Step-by-step explanation:

Reciprocal of 7/sqrt(98) = sqrt(98)/7 = √98/7

One-half of the reciprocal = 1/2 × √98/7 = √98/14 = 7√2/14 = √2/2