Math, asked by squareroot1, 1 year ago

simplify the product 3root2 *4 root2*12 root 32

Answers

Answered by sahanuj703
158

Answer:

2 is correct answer. And l hope, you will be understood.

Attachments:
Answered by Dhruv4886
27

Given:

3root2 *4 root2*12 root 32

To Find:

Simplify the product

Solution:

First, let the whole expression be equal to x then we can express it in,

x=3\sqrt{2} *4\sqrt{2}*12\sqrt{32}

Now let us club the whole numbers together and the root numbers together separating them by bracket so we can deal with them separately

x=(3*4*12)(\sqrt{2} *\sqrt{2} *\sqrt{32} )

Now multiply the whole numbers together and the numbers with root multiply them together with an under root on them

x=144*\sqrt{128}

Now we should know that when a number is about to be sent inside an under root then the number becomes its square inside the root, so in this case, too we will take 144 squared multiplied by 128 whole under a root

x=\sqrt{144^2*128} \\=\sqrt{2654208}

Now we will need to prime factorize the number and form a pair of two prime numbers that will come outside the root and which are left behind will stay in

2654208= 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3

So we can equate it like

x=2^7*3^2*\sqrt{2} \\=1152\sqrt{2}

Hence, the value of the expression is 1152root2.

Similar questions