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Q: Why is the square root of a sum equals the sum of the square roots?

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The square root of 100 = 10 The square root of 225 = 15 The sum = 10 + 15 = 25

Assuming the roots are positive, then ~ 15.59.

No. The right hand side is always greater - unless both components are zero.

I'm assuming that you mean 'square root'. Yes, this sum is irrational. So are each of the two numbers alone. A simple proof can be done by writing x=square root 2 + square root 3 and then "squareing away" the square roots and then use the rational roots theorem. The sum or difference of two irrational number need not be irrational! Look at sqrt(2)- sqrt(2)=0 which is rational.

to find the root-sum square of n numbers you square each number, add them, then take square root of sum For exanple root sum square of 2,3, and 4 is square root of (4+9+16) = sqrt(29) = 5.39

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sqrt(15) + sqrt(25) = 5 + sqrt(15) = 8.873 (using principal roots only).

The sum of a [single] square equals the square.

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No. The Square root of x is not the value of x. So it can not be simplified beyond: Root X + root 3x Yes. The square root of 3x equals the square root of 3 times the square root of x, so when you add another square root of x, you can factor out the square root of x, thereby simplifying the expression to the square root of x times the sum of one plus the square root of three.

You can. Just add the numbers together, and find their square root. One plus three is four; the square root of the sum is two.

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