Simplify (-3+ square root of 175)(-5+ square root of 7)

$(- 3 + \sqrt{175}) (- 5 + \sqrt{7})$

Step 1

Simplify each term.

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$(- 3 + \sqrt{25 (7)}) (- 5 + \sqrt{7})$

Rewrite $25$ as $5^{2}$ .

$(- 3 + \sqrt{5^{2} \cdot 7}) (- 5 + \sqrt{7})$

Pull terms out from under the radical.

$(- 3 + 5 \sqrt{7}) (- 5 + \sqrt{7})$

Step 2

Expand $(- 3 + 5 \sqrt{7}) (- 5 + \sqrt{7})$ using the FOIL Method.

Apply the distributive property.

$- 3 (- 5 + \sqrt{7}) + 5 \sqrt{7} (- 5 + \sqrt{7})$

Apply the distributive property.

$- 3 \cdot - 5 - 3 \sqrt{7} + 5 \sqrt{7} (- 5 + \sqrt{7})$

Apply the distributive property.

$- 3 \cdot - 5 - 3 \sqrt{7} + 5 \sqrt{7} \cdot - 5 + 5 \sqrt{7} \sqrt{7}$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $- 3$ by $- 5$ .

$15 - 3 \sqrt{7} + 5 \sqrt{7} \cdot - 5 + 5 \sqrt{7} \sqrt{7}$

Multiply $- 5$ by $5$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 \sqrt{7} \sqrt{7}$

Multiply $5 \sqrt{7} \sqrt{7}$ .

Raise $\sqrt{7}$ to the power of $1$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 ({\sqrt{7}}^{1} \sqrt{7})$

Raise $\sqrt{7}$ to the power of $1$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 {\sqrt{7}}^{1 + 1}$

Add $1$ and $1$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 {\sqrt{7}}^{2}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 {(7^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 \cdot 7^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 \cdot 7^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 \cdot 7^{\frac{2}{2}}$

Rewrite the expression.

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 \cdot 7^{1}$

Evaluate the exponent.

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 5 \cdot 7$

Multiply $5$ by $7$ .

$15 - 3 \sqrt{7} - 25 \sqrt{7} + 35$

Add $15$ and $35$ .

$50 - 3 \sqrt{7} - 25 \sqrt{7}$

Subtract $25 \sqrt{7}$ from $- 3 \sqrt{7}$ .

$50 - 28 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$50 - 28 \sqrt{7}$

Decimal Form:

$- 24.08103670 \dots$

Simplify (-3+ square root of 175)(-5+ square root of 7)

Related Questions

Support LCMGCF.com by disabling your adblocker.