Solve 4root3x^25x-2root3

Question

Simplify the expression

60 x^{2} - 23

Evaluate

4 (3 x)^{2} \times 5 x - 23

Solution

More Steps

Evaluate

4 (3 x)^{2} \times 5 x

Multiply the terms

20 (3 x)^{2} x

Multiply the terms

More Steps

Evaluate

20 (3 x)^{2}

Rewrite the expression

20 \times 3 x

Multiply the numbers

60 x

60 x \times x

Multiply the terms

60 x^{2}

60 x^{2} - 23

Show Solution

Factor the expression

2 (30 x^{2} - 3)

Evaluate

4 (3 x)^{2} \times 5 x - 23

Multiply

More Steps

Evaluate

4 (3 x)^{2} \times 5 x

Multiply the terms

20 (3 x)^{2} x

Multiply the terms

More Steps

Evaluate

20 (3 x)^{2}

Rewrite the expression

20 \times 3 x

Multiply the numbers

60 x

60 x \times x

Multiply the terms

60 x^{2}

60 x^{2} - 23

Solution

2 (30 x^{2} - 3)

Show Solution

Find the roots

x = \frac{4 2700}{30}

Alternative Form

x \approx 0.240281

Evaluate

4 (3 x)^{2} \times 5 x - 23

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

4 (3 x)^{2} \times 5 x - 23 = 0

Find the domain

4 (3 x)^{2} \times 5 x - 23 = 0, x \geq 0

Calculate

4 (3 x)^{2} \times 5 x - 23 = 0

Multiply

More Steps

Multiply the terms

4 (3 x)^{2} \times 5 x

Multiply the terms

20 (3 x)^{2} x

Multiply the terms

More Steps

Evaluate

20 (3 x)^{2}

Rewrite the expression

20 \times 3 x

Multiply the numbers

60 x

60 x \times x

Multiply the terms

60 x^{2}

60 x^{2} - 23 = 0

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

60 x^{2} = 0 + 23

Add the terms

60 x^{2} = 23

Divide both sides

\frac{60 x ^{2}}{60} = \frac{2 3}{60}

Divide the numbers

x^{2} = \frac{2 3}{60}

Cancel out the common factor 2

x^{2} = \frac{3}{30}

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

x = \pm \frac{3}{30}

Simplify the expression

More Steps

Evaluate

\frac{3}{30}

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

\frac{3}{30}

Simplify the radical expression

More Steps

Evaluate

3

Use m n a = mn a to simplify the expression

2 \times 2 3

Multiply the numbers

43

\frac{4 3}{30}

Multiply by the Conjugate

\frac{4 3 \times 30}{30 \times 30}

Multiply the numbers

More Steps

Evaluate

43 \times 30

Use n a = mn a^{m} to expand the expression

43 \times 4 3 0^{2}

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

4 3 \times 3 0^{2}

Calculate the product

42700

\frac{4 2700}{30 \times 30}

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

\frac{4 2700}{30}

x = \pm \frac{4 2700}{30}

Separate the equation into 2 possible cases

x = \frac{4 2700}{30} x = - \frac{4 2700}{30}

Check if the solution is in the defined range

x = \frac{4 2700}{30} x = - \frac{4 2700}{30}, x \geq 0

Solution

x = \frac{4 2700}{30}

Alternative Form

x \approx 0.240281

Show Solution