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
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.
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.
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.
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)
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