1Cademy - Simplifying $$5 + \sqrt{75}$$ and $$2 + \sqrt{98}$$

Learn Before

Simplifying $3 + \sqrt{32}$

Example

Simplifying $5 + \sqrt{75}$ and $2 + \sqrt{98}$

Simplify sums involving an integer and a square root by extracting the largest perfect square factor from the radical. ⓐ $5 + \sqrt{75}$ : Rewrite the radicand using its largest perfect square factor, which is $25$ . Simplify the radical: $\sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3}$ . Substitute this back into the expression to obtain $5 + 5\sqrt{3}$ . The integer and the radical term cannot be added together because they are not like terms. ⓑ $2 + \sqrt{98}$ : Find the largest perfect square factor of $98$ , which is $49$ . Simplify the radical: $\sqrt{98} = \sqrt{49 \cdot 2} = 7\sqrt{2}$ . Substitute this back to get $2 + 7\sqrt{2}$ . As before, these two terms cannot be combined as one has a radical and the other does not.

Updated 2026-05-01

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related