Products of Irrational Square Roots Quick Check

Question

1 of 51 of 5 Items
Question
Rewrite the irrational square root √48
as the product of an integer and another irrational square root.(1 point)
Responses

√43
4 start root 3 end root

√224
2 start root 24 end root

√412
4 start root 12 end root

√212
2 start root 12 end root

Answer 1

To rewrite the irrational square root \( \sqrt{48} \) as the product of an integer and another irrational square root, we can simplify it step by step.

1. Factor \( 48 \) into its prime factors:

   • \( 48 = 16 \times 3 \)
   • Here, \( 16 \) is a perfect square.

2. Rewrite \( \sqrt{48} \): \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]

So, the correct answer is: \[ 4\sqrt{3} \]

Therefore, the option you are looking for is:

• 4 start root 3 end root.