Solve 60^2+68^2=a^2

$$60 ^ { 2 } + 68 ^ { 2 } = a ^ { 2 }$$

Solve for a

$$a=4\sqrt{514}\approx 90.68627239$$

$$a=-4\sqrt{514}\approx -90.68627239$$

Steps by Finding Square Root

Calculate 60 to the power of 2 and get 3600.

$$3600+68^{2}=a^{2}$$

Calculate 68 to the power of 2 and get 4624.

$$3600+4624=a^{2}$$

Add 3600 and 4624 to get 8224.

$$8224=a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}=8224$$

Take the square root of both sides of the equation.

$$a=4\sqrt{514} a=-4\sqrt{514}$$

Steps Using the Quadratic Formula

Calculate 60 to the power of 2 and get 3600.

$$3600+68^{2}=a^{2}$$

Calculate 68 to the power of 2 and get 4624.

$$3600+4624=a^{2}$$

Add 3600 and 4624 to get 8224.

$$8224=a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}=8224$$

Subtract 8224 from both sides.

$$a^{2}-8224=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -8224 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-8224\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-8224\right)}}{2}$$

Multiply -4 times -8224.

$$a=\frac{0±\sqrt{32896}}{2}$$

Take the square root of 32896.

$$a=\frac{0±8\sqrt{514}}{2}$$

Now solve the equation a=\frac{0±8\sqrt{514}}{2} when ± is plus.

$$a=4\sqrt{514}$$

Now solve the equation a=\frac{0±8\sqrt{514}}{2} when ± is minus.

$$a=-4\sqrt{514}$$

The equation is now solved.

$$a=4\sqrt{514} a=-4\sqrt{514}$$