Radical Expressions and Equations Flashcards

Question 1

What is the principal square root of a real number $a$?

Accepted Answer

The principal square root $\sqrt{a}$ is the unique nonnegative number $r$ such that $r^2=a$ (defined for $a\ge 0$ in the reals).

Question 2

Simplify $(2\sqrt{3})(5\sqrt{12})$.

Accepted Answer

$$ (2\sqrt{3})(5\sqrt{12})=10\sqrt{36}=60 $$

Question 3

Solve $\sqrt{x+5}=x-1$ and state any restrictions.

Accepted Answer

Restriction: $x-1\ge 0$ and $x+5\ge 0$ so $x\ge 1$. Squaring gives $x+5=(x-1)^2=x^2-2x+1$, so $x^2-3x-4=0$, $x=4$ or $x=-1$. Check: $x=4$ works; $x=-1$ violates $x\ge 1$. Solution: $x=4$.

Radical Expressions and Equations Flashcards

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