Question

positive square root value of root 32 minus root 24

Answer 1

value is 56-32 root 3

Answer 2

$\sqrt{32} -\sqrt{24}$  =  $4 \sqrt{2} - 2\sqrt{6}$  = 0.74.

Step-by-step explanation:

We have to find the positive square root value of root 32 minus root 24.

The given expression is: $\sqrt{32} -\sqrt{24}$

The factorization of number 32 is;

32 = 2 $\times$ 16

16 = 2 $\times$ 8

8 = 2 $\times$ 4

4 = 2 $\times$ 2

2 = 2 $\times$ 1

So, the prime factorization of 32 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2.

Similarly, the factorization of number 24 is;

24 = 2 $\times$ 12

12 = 2 $\times$ 6

6 = 2 $\times$ 3

3 = 3 $\times$ 1

So, the prime factorization of 24 = 2 $\times$ 2 $\times$ 2 $\times$ 3.

Putting these factorizations inside the root we get;

$\sqrt{32} -\sqrt{24}$  =  $\sqrt{2 \times 2 \times 2 \times 2 \times 2 } -\sqrt{2 \times 2 \times 2 \times 3}$

                  =  $(2 \times 2) \sqrt{2} - 2 \sqrt{2 \times 3}$

                  =  $4 \sqrt{2} - 2\sqrt{6}$

                  =  $2(2\sqrt{2} -\sqrt{6} )$

As we know that : $\sqrt{2}$ = 1.41  and  $\sqrt{6}$ = 2.45    {rounding to 2 decimal points}

So, $\sqrt{32} -\sqrt{24}$  =  2 $\times$ ($2 \times 1.41 - 2.45$)

                         =  2 $\times$ 0.37 = 0.74