Solve for d 140=356 square root of d

$140 = 356 \sqrt{d}$

Step 1

Rewrite the equation as $356 \sqrt{d} = 140$ .

$356 \sqrt{d} = 140$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${(356 \sqrt{d})}^{2} = 140^{2}$

Step 3

Simplify each side of the equation.

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

${(356 d^{\frac{1}{2}})}^{2} = 140^{2}$

Simplify the left side.

Simplify ${(356 d^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $356 d^{\frac{1}{2}}$ .

$356^{2} {(d^{\frac{1}{2}})}^{2} = 140^{2}$

Raise $356$ to the power of $2$ .

$126736 {(d^{\frac{1}{2}})}^{2} = 140^{2}$

Multiply the exponents in ${(d^{\frac{1}{2}})}^{2}$ .

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

$126736 d^{\frac{1}{2} \cdot 2} = 140^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$126736 d^{\frac{1}{2} \cdot 2} = 140^{2}$

Rewrite the expression.

$126736 d^{1} = 140^{2}$

Simplify.

$126736 d = 140^{2}$

Simplify the right side.

Raise $140$ to the power of $2$ .

$126736 d = 19600$

Step 4

Divide each term in $126736 d = 19600$ by $126736$ and simplify.

Divide each term in $126736 d = 19600$ by $126736$ .

$\frac{126736 d}{126736} = \frac{19600}{126736}$

Simplify the left side.

Cancel the common factor of $126736$ .

Cancel the common factor.

$\frac{126736 d}{126736} = \frac{19600}{126736}$

Divide $d$ by $1$ .

$d = \frac{19600}{126736}$

Simplify the right side.

Cancel the common factor of $19600$ and $126736$ .

Factor $16$ out of $19600$ .

$d = \frac{16 (1225)}{126736}$

Cancel the common factors.

Factor $16$ out of $126736$ .

$d = \frac{16 \cdot 1225}{16 \cdot 7921}$

Cancel the common factor.

$d = \frac{16 \cdot 1225}{16 \cdot 7921}$

Rewrite the expression.

$d = \frac{1225}{7921}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = \frac{1225}{7921}$

Decimal Form:

$d = 0.15465219 \dots$

Solve for d 140=356 square root of d

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