Question

Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight.

eleven square root of two minus five square root of seven

eleven square root of four minus five square root of fourteen

six square root of five

six square root of nine

Answer 1

a

Explanation:

9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}

Now, \sqrt{8} = \sqrt{2 \times 2 \times 2} = 2\sqrt{2}

\sqrt{28} = \sqrt{2 \times 2 \times 7} = 2\sqrt{7}

∴ 9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}

= 9\sqrt{2} - 3\sqrt{7} + 2\sqrt{2} - 2\sqrt{7}

= 9\sqrt{2} + 2\sqrt{2} - 3\sqrt{7} - 2\sqrt{7}

= 11\sqrt{2} - 5\sqrt{7}

Answer 2

`11√(2) - 5√(7)`

Option (A) is the correct answer.

Explanation:

`9√(2) - 3√(7) + √(8) - √(28)`

Now,
`√(8) = √(2 * 2 * 2) = 2√(2)`

`√(28) = √(2 * 2 * 7) = 2√(7)`

∴
`9√(2) - 3√(7) + √(8) - √(28)`

=
`9√(2) - 3√(7) + 2√(2) - 2√(7)`

=
`9√(2) + 2√(2) - 3√(7) - 2√(7)`

=
`11√(2) - 5√(7)`

Therefore option (a) is the correct answer.