What is the answer to 2 1/4 =x^{1/2} ?

The answer to 2 1/4 =x^{1/2} is x=5 1/16

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2 1/4 =x^{1/2}

2 \frac{1}{4} = x^{\frac{1}{2}}

x = 5 \frac{1}{16}

Decimal Notation

x = 5.0625

Solution steps

2 \frac{1}{4} = x^{\frac{1}{2}}

Convert mixed numbers to improper fractions:

2 \frac{1}{4} = \frac{9}{4}

\frac{9}{4} = x^{\frac{1}{2}}

Square both sides:

\frac{81}{16} = x

\frac{81}{16} = x

Switch sides

x = \frac{81}{16}

Verify Solutions:

x = \frac{81}{16}

True

The solution is

x = \frac{81}{16}

Convert improper fractions to mixed numbers:

\frac{81}{16} = 5 \frac{1}{16}

x = 5 \frac{1}{16}

x - 45 + 20 = 25

4 x = 2 2 x - 3

2 x - 7 = x - 22

x + 3 + x = 3

x^{3} + 2000 = 2