Solve b1b72-11 - ScanMath

Question

Simplify the expression

72 b^{2} - 11

Evaluate

b \times 1 \times b \times 72 - 11

Solution

More Steps

Evaluate

b \times 1 \times b \times 72

Rewrite the expression

b \times b \times 72

Multiply the terms

b^{2} \times 72

Use the commutative property to reorder the terms

72 b^{2}

72 b^{2} - 11

Show Solution

b_{1} = - \frac{22}{12}, b_{2} = \frac{22}{12}

Alternative Form

b_{1} \approx - 0.390868, b_{2} \approx 0.390868

Evaluate

b \times 1 \times b \times 72 - 11

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

b \times 1 \times b \times 72 - 11 = 0

Multiply the terms

More Steps

Multiply the terms

b \times 1 \times b \times 72

Rewrite the expression

b \times b \times 72

Multiply the terms

b^{2} \times 72

Use the commutative property to reorder the terms

72 b^{2}

72 b^{2} - 11 = 0

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

72 b^{2} = 0 + 11

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

72 b^{2} = 11

Divide both sides

\frac{72 b ^{2}}{72} = \frac{11}{72}

Divide the numbers

b^{2} = \frac{11}{72}

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

b = \pm \frac{11}{72}

Simplify the expression

More Steps

Evaluate

\frac{11}{72}

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

\frac{11}{72}

Simplify the radical expression

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Evaluate

72

Write the expression as a product where the root of one of the factors can be evaluated

36 \times 2

Write the number in exponential form with the base of 6

6^{2} \times 2

The root of a product is equal to the product of the roots of each factor

6^{2} \times 2

Reduce the index of the radical and exponent with 2

62

\frac{11}{6 2}

Multiply by the Conjugate

\frac{11 \times 2}{6 2 \times 2}

Multiply the numbers

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Evaluate

11 \times 2

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

11 \times 2

Calculate the product

22

\frac{22}{6 2 \times 2}

Multiply the numbers

More Steps

Evaluate

62 \times 2

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

6 \times 2

Multiply the terms

12

\frac{22}{12}

b = \pm \frac{22}{12}

Separate the equation into 2 possible cases

b = \frac{22}{12} b = - \frac{22}{12}

Solution

b_{1} = - \frac{22}{12}, b_{2} = \frac{22}{12}

Alternative Form

b_{1} \approx - 0.390868, b_{2} \approx 0.390868

Show Solution