# Solving Square Root Problems: 10^2+10^2 to 10*√(2)

• christian0710
In summary, the square root of the sum of two numbers squared can be simplified to the product of the square root of the number squared and the square root of 2. This principle can also be applied to the sum of three numbers squared, where the square root of the sum can be simplified to the product of the square root of the number squared and the square root of 3.
christian0710
Hi I'm just wondering: How does √(10^2+10^2) become 10*√(2) ? I also noticed that √(10^2+10^2+ 10^2) becomed 10*√(3) But how to you mathematically - ith more steps- go from √(10^2+10^2) to 10*√(2)?

Kind regards,
Christian

Well, what do you get when you add a number to itself?

christian0710
christian0710 said:
Hi I'm just wondering: How does √(10^2+10^2) become 10*√(2) ? I also noticed that √(10^2+10^2+ 10^2) becomed 10*√(3) But how to you mathematically - ith more steps- go from √(10^2+10^2) to 10*√(2)?

Kind regards,
Christian

These rules apply:

$$\sqrt{ab}=\sqrt{a}\sqrt{b}$$

$$ab+ac=a(b+c)$$

christian0710
Ohh of course! thank you very much :)
So it's

sqrt(10^2 +10^2) = sqrt(2*10^2) = sqrt(10^2)*sqrt(2)= 10*sqrt(2).

Mentallic
##\sqrt{10^2+10^2}##

##\sqrt{a^2+a^2}=\sqrt{2a^2}##

Similarly

##\sqrt{10^2+10^2}=\sqrt{2(10)^2}##

##\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}##

Similarly
##=\sqrt{2(10)^2}=\sqrt{2}\cdot\sqrt{10^2}##

##=10\sqrt{2}##

## 1. How do you solve square root problems?

To solve square root problems, you need to find the number that, when multiplied by itself, gives the original number. This can be done by using a calculator or by using a method called "prime factorization" where you break down the number into its prime factors and then take the square root of the perfect squares.

## 2. What is the process for solving "10^2+10^2 to 10*√(2)"?

The process for solving "10^2+10^2 to 10*√(2)" is as follows:1. Simplify 10^2+10^2 to get 100+100=2002. Take the square root of 200 using a calculator or the prime factorization method. The square root of 200 is approximately 14.142.3. Multiply 10 by √(2) to get 10*√(2)=10*1.414=14.144. The final answer is 14.14.

## 3. What is the purpose of solving square root problems?

The purpose of solving square root problems is to find the missing side or dimension of a square or rectangle, or to find the value of a variable in an equation that involves square roots.

## 4. What are some common mistakes to avoid when solving square root problems?

Some common mistakes to avoid when solving square root problems are:- Forgetting to simplify before taking the square root- Incorrectly using the square root and exponent rules- Using the wrong operation (multiplication instead of division or vice versa)- Not checking for extraneous solutions (solutions that do not work in the original equation)

## 5. Are there any tips or tricks for solving square root problems?

Some tips and tricks for solving square root problems include:- Familiarizing yourself with perfect squares (numbers whose square roots are whole numbers)- Using estimation to get a rough idea of the answer before using a calculator- Practicing regularly to improve your mental math skills for square roots- Checking your answer by squaring it to make sure it equals the original number

Replies
3
Views
898
Replies
15
Views
1K
Replies
6
Views
1K
Replies
2
Views
2K
Replies
1
Views
1K
Replies
8
Views
516
Replies
2
Views
2K
Replies
13
Views
4K
Replies
5
Views
908
Replies
8
Views
1K