# Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4: 50

$\sqrt 7$

#### Work Step by Step

We start with $\sqrt 63$ - $\sqrt 28$ We can write 63 as 9 x 7 ( a perfect square times a number) We can write 28 as 4 x 7 (a perfect square times a number) Rewriting the problem, we have: $\sqrt{ 9\cdot 7}$ - $\sqrt {4 \cdot 7}$ We can take the square root of 9 and of 4; this gives us 3 and 2. Once we take the square root of a number under a radical sign, the square root is written on the outside of the radical, like this: 3$\sqrt 7$ - 2$\sqrt 7$ We can now subtract (since the radical parts are exactly alike). We get $\sqrt 7$

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