Math / Algebra

QuestionSimplify the radical expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$

Studdy Solution

STEP 1

1. The expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$ involves square roots and algebraic fractions.
2. The expression can be simplified using properties of square roots and exponents.
3. The final expression should be simplified as much as possible.

STEP 2

1. Simplify the fraction inside the square root.
2. Apply the square root to both the numerator and the denominator separately.
3. Simplify the resulting expression.

STEP 3

Simplify the fraction inside the square root.
$\frac{2 x^{2}}{9 y^{4}} \text{ is already in its simplest form.}$

STEP 4

Apply the square root to both the numerator and the denominator separately.
$\sqrt{\frac{2 x^{2}}{9 y^{4}}} = \frac{\sqrt{2 x^{2}}}{\sqrt{9 y^{4}}}$

STEP 5

Simplify the square root of the numerator.
$\sqrt{2 x^{2}} = \sqrt{2} \cdot \sqrt{x^{2}} = \sqrt{2} \cdot x$

STEP 6

Simplify the square root of the denominator.
$\sqrt{9 y^{4}} = \sqrt{9} \cdot \sqrt{y^{4}} = 3 \cdot y^{2}$

STEP 7

Combine the simplified numerator and denominator to obtain the final expression.
$\frac{\sqrt{2} \cdot x}{3 \cdot y^{2}} = \frac{x \sqrt{2}}{3 y^{2}}$
Solution: $\sqrt{\frac{2 x^{2}}{9 y^{4}}} = \frac{x \sqrt{2}}{3 y^{2}}$

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QuestionSimplify the radical expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$

Studdy Solution

STEP 1

1. The expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$ involves square roots and algebraic fractions.
2. The expression can be simplified using properties of square roots and exponents.
3. The final expression should be simplified as much as possible.

STEP 2

1. Simplify the fraction inside the square root.
2. Apply the square root to both the numerator and the denominator separately.
3. Simplify the resulting expression.

STEP 3

Simplify the fraction inside the square root.
$\frac{2 x^{2}}{9 y^{4}} \text{ is already in its simplest form.}$

STEP 4

Apply the square root to both the numerator and the denominator separately.
$\sqrt{\frac{2 x^{2}}{9 y^{4}}} = \frac{\sqrt{2 x^{2}}}{\sqrt{9 y^{4}}}$

STEP 5

Simplify the square root of the numerator.
$\sqrt{2 x^{2}} = \sqrt{2} \cdot \sqrt{x^{2}} = \sqrt{2} \cdot x$

STEP 6

Simplify the square root of the denominator.
$\sqrt{9 y^{4}} = \sqrt{9} \cdot \sqrt{y^{4}} = 3 \cdot y^{2}$

STEP 7

Combine the simplified numerator and denominator to obtain the final expression.
$\frac{\sqrt{2} \cdot x}{3 \cdot y^{2}} = \frac{x \sqrt{2}}{3 y^{2}}$
Solution: $\sqrt{\frac{2 x^{2}}{9 y^{4}}} = \frac{x \sqrt{2}}{3 y^{2}}$

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QuestionSimplify the radical expression 2x29y4\sqrt{\frac{2 x^{2}}{9 y^{4}}}9y42x2​​

Studdy Solution

STEP 1

1. The expression 2x29y4\sqrt{\frac{2 x^{2}}{9 y^{4}}}9y42x2​​ involves square roots and algebraic fractions.2. The expression can be simplified using properties of square roots and exponents.3. The final expression should be simplified as much as possible.

STEP 2

1. Simplify the fraction inside the square root.2. Apply the square root to both the numerator and the denominator separately.3. Simplify the resulting expression.

STEP 3

Simplify the fraction inside the square root.2x29y4 is already in its simplest form. \frac{2 x^{2}}{9 y^{4}} \text{ is already in its simplest form.} 9y42x2​ is already in its simplest form.

STEP 4

Apply the square root to both the numerator and the denominator separately.2x29y4=2x29y4 \sqrt{\frac{2 x^{2}}{9 y^{4}}} = \frac{\sqrt{2 x^{2}}}{\sqrt{9 y^{4}}} 9y42x2​​=9y4​2x2​​

STEP 5

Simplify the square root of the numerator.2x2=2⋅x2=2⋅x \sqrt{2 x^{2}} = \sqrt{2} \cdot \sqrt{x^{2}} = \sqrt{2} \cdot x 2x2​=2​⋅x2​=2​⋅x

STEP 6

Simplify the square root of the denominator.9y4=9⋅y4=3⋅y2 \sqrt{9 y^{4}} = \sqrt{9} \cdot \sqrt{y^{4}} = 3 \cdot y^{2} 9y4​=9​⋅y4​=3⋅y2

STEP 7

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QuestionSimplify the radical expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$

1. The expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$ involves square roots and algebraic fractions.
2. The expression can be simplified using properties of square roots and exponents.
3. The final expression should be simplified as much as possible.

1. Simplify the fraction inside the square root.
2. Apply the square root to both the numerator and the denominator separately.
3. Simplify the resulting expression.

Simplify the fraction inside the square root.
$\frac{2 x^{2}}{9 y^{4}} \text{ is already in its simplest form.}$

Apply the square root to both the numerator and the denominator separately.
$\sqrt{\frac{2 x^{2}}{9 y^{4}}} = \frac{\sqrt{2 x^{2}}}{\sqrt{9 y^{4}}}$

Simplify the square root of the numerator.
$\sqrt{2 x^{2}} = \sqrt{2} \cdot \sqrt{x^{2}} = \sqrt{2} \cdot x$

Simplify the square root of the denominator.
$\sqrt{9 y^{4}} = \sqrt{9} \cdot \sqrt{y^{4}} = 3 \cdot y^{2}$