Solve 9v^2004-30 - Socratic AI (ScanMath)

Question

Simplify the expression

36 v^{2} - 30

Evaluate

9 v^{2} \times 4 - 30

Solution

36 v^{2} - 30

Show Solution

6 (6 v^{2} - 5)

Evaluate

9 v^{2} \times 4 - 30

Multiply the terms

36 v^{2} - 30

Solution

6 (6 v^{2} - 5)

Show Solution

v_{1} = - \frac{30}{6}, v_{2} = \frac{30}{6}

Alternative Form

v_{1} \approx - 0.912871, v_{2} \approx 0.912871

Evaluate

9 v^{2} \times 4 - 30

To find the roots of the expression,set the expression equal to 0

9 v^{2} \times 4 - 30 = 0

Multiply the terms

36 v^{2} - 30 = 0

Move the constant to the right-hand side and change its sign

36 v^{2} = 0 + 30

Removing 0 doesn't change the value,so remove it from the expression

36 v^{2} = 30

Divide both sides

\frac{36 v ^{2}}{36} = \frac{30}{36}

Divide the numbers

v^{2} = \frac{30}{36}

Cancel out the common factor 6

v^{2} = \frac{5}{6}

Take the root of both sides of the equation and remember to use both positive and negative roots

v = \pm \frac{5}{6}

Simplify the expression

More Steps

Evaluate

\frac{5}{6}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5}{6}

Multiply by the Conjugate

\frac{5 \times 6}{6 \times 6}

Multiply the numbers

More Steps

Evaluate

5 \times 6

The product of roots with the same index is equal to the root of the product

5 \times 6

Calculate the product

30

\frac{30}{6 \times 6}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{30}{6}

v = \pm \frac{30}{6}

Separate the equation into 2 possible cases

v = \frac{30}{6} v = - \frac{30}{6}

Solution

v_{1} = - \frac{30}{6}, v_{2} = \frac{30}{6}

Alternative Form

v_{1} \approx - 0.912871, v_{2} \approx 0.912871

Show Solution