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Solve the equation given below for x.

x2 = 56/36

13 answers

To solve the equation \( x^2 = \frac{56}{36} \), we first simplify the fraction on the right side.

  1. Simplifying \( \frac{56}{36} \):

    • The greatest common divisor (GCD) of 56 and 36 is 4.
    • Dividing both the numerator and denominator by 4:

    \[ \frac{56 \div 4}{36 \div 4} = \frac{14}{9} \]

So, we have:

\[ x^2 = \frac{14}{9} \]

  1. To solve for \( x \), we take the square root of both sides:

\[ x = \pm \sqrt{\frac{14}{9}} \]

  1. We can simplify this further:

\[ x = \pm \frac{\sqrt{14}}{\sqrt{9}} = \pm \frac{\sqrt{14}}{3} \]

Thus, the solutions for \( x \) are:

\[ x = \frac{\sqrt{14}}{3} \quad \text{and} \quad x = -\frac{\sqrt{14}}{3} \]

Simplify sqrt 81

The square root of 81 is calculated as follows:

\[ \sqrt{81} = 9 \]

Therefore, \(\sqrt{81}\) simplifies to \(9\).

Which of the following best describes the solution to the equation below?

x2 = 3
Note: Only consider the positive solution.

A.
It is a rational number.

B.
It is greater than zero but less than one.

C.
It is a repeating decimal.

D.
It is an irrational number.

To solve the equation \( x^2 = 3 \), we take the square root of both sides:

\[ x = \sqrt{3} \]

Now, let's analyze \( \sqrt{3} \):

  1. Rational Number: A rational number can be expressed as the quotient of two integers. Since \( \sqrt{3} \) cannot be expressed this way, it is not a rational number.

  2. Greater than Zero but Less than One: The value of \( \sqrt{3} \) is approximately \( 1.732 \), which is greater than one, so this option is not correct.

  3. Repeating Decimal: A repeating decimal is a decimal that eventually repeats a sequence of digits. Since \( \sqrt{3} \) is approximately \( 1.73205... \) and does not repeat, this option is also incorrect.

  4. Irrational Number: An irrational number cannot be expressed as a fraction of two integers, and the decimal representation of an irrational number does not terminate or repeat. Since \( \sqrt{3} \) fits this description, it is an irrational number.

Therefore, the best description of the positive solution \( \sqrt{3} \) is:

D. It is an irrational number.

Solve the equation for x.

x3 = 125/27

To solve the equation

\[ x^3 = \frac{125}{27}, \]

we need to take the cube root of both sides.

  1. Taking the Cube Root:

\[ x = \sqrt[3]{\frac{125}{27}}. \]

  1. Simplifying the Cube Root:

We can separate the cube root of the fraction as follows:

\[ x = \frac{\sqrt[3]{125}}{\sqrt[3]{27}}. \]

  1. Calculating the Cube Roots:
  • The cube root of \(125\) is \(5\) since \(5^3 = 125\).
  • The cube root of \(27\) is \(3\) since \(3^3 = 27\).

So we have:

\[ x = \frac{5}{3}. \]

Thus, the solution to the equation \(x^3 = \frac{125}{27}\) is

\[ x = \frac{5}{3}. \]

Determine which of the following are solutions to the equation below

x2 = 1/81

To determine the solutions to the equation

\[ x^2 = \frac{1}{81}, \]

we need to take the square root of both sides.

  1. Taking the Square Root:

\[ x = \pm \sqrt{\frac{1}{81}}. \]

  1. Simplifying the Square Root:

We can separate the square root of the fraction:

\[ x = \pm \frac{\sqrt{1}}{\sqrt{81}}. \]

  1. Calculating the Square Roots:
  • The square root of \(1\) is \(1\).
  • The square root of \(81\) is \(9\) since \(9^2 = 81\).

So we have:

\[ x = \pm \frac{1}{9}. \]

Thus, the solutions to the equation \(x^2 = \frac{1}{81}\) are

\[ x = \frac{1}{9} \quad \text{and} \quad x = -\frac{1}{9}. \]

Both of these values are valid solutions to the equation.

Determine which of the following is the solution to the equation below.

x3 = 10

To determine the solution to the equation

\[ x^3 = 10, \]

we need to take the cube root of both sides.

  1. Taking the Cube Root:

\[ x = \sqrt[3]{10}. \]

This expression represents the solution to the equation.

  1. Calculating the Cube Root:

The value of \(\sqrt[3]{10}\) is a numerical approximation. Since \(10\) is not a perfect cube, we can approximate it:

\[ \sqrt[3]{10} \approx 2.154. \]

Thus, the solution to the equation \(x^3 = 10\) is

\[ x = \sqrt[3]{10}, \]

which is approximately \(2.154\).

If you have multiple choice options, the exact expression \( \sqrt[3]{10} \) is the correct solution. If you need a numerical answer, it’s approximately \( 2.154 \).

Simplify 3 sqrt 1

To simplify \(3 \sqrt{1}\):

  1. Calculate \(\sqrt{1}\): \[ \sqrt{1} = 1 \]

  2. Multiply by 3: \[ 3 \sqrt{1} = 3 \times 1 = 3 \]

Therefore, \(3 \sqrt{1} = 3\).