Example Question - mathematically equivalent
Here are examples of questions we've helped users solve.
Finding Equivalent Expression for the Square Root
To find another name for the square root expression given, we should look for an expression that is mathematically equivalent. The original expression is: \( \sqrt{\frac{B}{J}} \) We're looking for an alternative expression that has the same value. Multiplying or dividing both the numerator and the denominator by the same nonzero number will keep the fraction equivalent. When we take the square root of a fraction, we can take the square root of the numerator and the denominator separately. Therefore, the expression can also be written as: \( \frac{\sqrt{B}}{\sqrt{J}} \) This corresponds to option C in the image provided: C) \( \frac{\sqrt{B}}{\sqrt{J}} \)
Solving Cube Root of 81x^10y^8
The expression in the image is the cube root of \((81x^{10}y^8)\), which can be written as \((81x^{10}y^8)^{\frac{1}{3}}\). To simplify this expression, we take the cube root of each factor separately: 1. The cube root of 81, which is \(3^4\), is 3, because \(3^3 = 27\) and \(3^3 \times 3 = 81\). 2. The cube root of \(x^{10}\) can be simplified by dividing the exponent by 3. This gives us \(x^{\frac{10}{3}}\) or \(x^3 \times x^{\frac{1}{3}}\). 3. The cube root of \(y^8\) can be simplified by dividing the exponent by 3. This gives us \(y^{\frac{8}{3}}\) or \(y^2 \times y^{\frac{2}{3}}\). Putting it all together, you get: \(3x^3x^{\frac{1}{3}}y^2y^{\frac{2}{3}}\) You can also leave it as \(3x^{\frac{10}{3}}y^{\frac{8}{3}}\) if you prefer. Both forms are mathematically equivalent.
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