Question

Please help!! Write in simplest radical form: √7/8 Show how you figured it out

Answer 1

Given expression:
`\sqrt{(7)/(8)}`.

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{(a)/(b)}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}`

`=(√(7))/(√(8))`

`√(8)=√(2^2\cdot \:2)=2√(2)`

`(√(7))/(√(8)) =(√(7))/(2√(2))`

`\mathrm{Rationalize\:}(√(7))/(2√(2))`

`\mathrm{Multiply\:by\:the\:conjugate}\:(√(2))/(√(2))`

`=(√(7)√(2))/(2√(2)√(2))`

`=(√(14))/(4)`

`=(√(14))/(4)`.