Question

Please help! Question is in picture. I will give Brainliest!!

Answer 1

Answer:

(d) They may be combines

Step-by-step explanation:

Given

$6\sqrt{32} - 12\sqrt{72}$

Required

Which option is true

Express 32 as 16 * 2 and 72 as 36 * 2

$6\sqrt{32} - 12\sqrt{72} = 6\sqrt{16 * 2} - 12\sqrt{36 * 2}$

Split

$6\sqrt{32} - 12\sqrt{72} = 6\sqrt{16} * \sqrt{2} - 12\sqrt{36} * \sqrt{2}$

This gives:

$6\sqrt{32} - 12\sqrt{72} = 6*4 * \sqrt{2} - 12*6 * \sqrt{2}$

$6\sqrt{32} - 12\sqrt{72} = 24 * \sqrt{2} - 72 * \sqrt{2}$

$6\sqrt{32} - 12\sqrt{72} = 24 \sqrt{2} - 72 \sqrt{2}$

Since both term have the same radicand, then:

$6\sqrt{32} - 12\sqrt{72} =( 24 - 72 )\sqrt{2}$

$6\sqrt{32} - 12\sqrt{72} =-48\sqrt{2}$

Option (d) is correct