Need help with some square root Simplifying

[gss1122]

Can some show me the process of simplifying square roots. Ex. the square root of 147.

 

[stapel]

The general process is to factor inside the radical, and then take out whatever you've got pairs of. For instance:

. . . . .\(\displaystyle \large{\sqrt{\mbox{ }25\mbox{ }}\mbox{ }=\mbox{ }\sqrt{\mbox{ }5\mbox{ }\times \mbox{ }5\mbox{ }}\mbox{ }=\mbox{ }5}\)


. . . . .\(\displaystyle \large{\sqrt{\mbox{ }75\mbox{ }}\mbox{ }=\mbox{ }\sqrt{\mbox{ }5\mbox{ }\times \mbox{ }5\mbox{ }\times \mbox{ }3\mbox{ }}\mbox{ }=\mbox{ }5\mbox{ }\sqrt{\mbox{ }3\mbox{ }}}\)


. . . . .\(\displaystyle \large{\sqrt{\mbox{ }1500\mbox{ }}\mbox{ }=\mbox{ }\sqrt{\mbox{ }2\mbox{ }\times \mbox{ }2\mbox{ }\times \mbox{ }3\mbox{ }\times \mbox{ }5\mbox{ }\times \mbox{ }5\mbox{ }\times \mbox{ }5\mbox{ }}\mbox{ }=\mbox{ }2\mbox{ }\times \mbox{ }5\mbox{ }\sqrt{\mbox{ }3\mbox{ }\times \mbox{ }5\mbox{ }}\mbox{ }=\mbox{ }10\mbox{ }\sqrt{\mbox{ }15\mbox{ }}}\)

Follow this same process with your example.

Eliz.

 

[gss1122]

so the answer is 3 radical 7 or 3√7 ??

 

[pka]

Do you understand how to use recursive definitions?
If N is the number of which we want the square root then here what we will do.
First define a first number R<SUB>1</SUB>=1.
Then for every k bigger than 1, define R<SUB>k</SUB>=[R<SUB>k-1</SUB>+(N/ R<SUB>k−1</SUB>)]/2.
When you calculate say 10 of these, you get close to the square root or N.

 

[Daniel_Feldman]

so the answer is 3 radical 7 or 3√7 ??

Other way around actually

√147=√(49 x 3)=7√3

 

[gss1122]

oh my mistake!! sry :lol: