Question

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

Answer 1

Answer:

a

Step-by-step 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

Answer:

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

Option (A) is the correct answer.

Step-by-step explanation:

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

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

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

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

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

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

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

Therefore option (a) is the correct answer.