# Question Video: Evaluating Algebraic Expressions Involving Square Roots in a Real-World Context Mathematics

The speed 𝑣, in feet per second, of an ocean wave at depth 𝑑, in feet, is given by the formula 𝑣 = √32𝑑. Determine, to the nearest tenth, the speed of an ocean wave at a depth of 11 feet.

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### Video Transcript

The speed 𝑣, in feet per second, of an ocean wave at depth 𝑑, in feet, is given by the formula 𝑣 is equal to the square root of 32𝑑. Determine, to the nearest tenth, the speed of an ocean wave at a depth of 11 feet.

In this question, we are given the formula 𝑣 is equal to the square root of 32𝑑, where 𝑣 is the speed in feet per second and 𝑑 is the depth in feet. We need to calculate the speed 𝑣 when the depth is 11 feet. We need to substitute 𝑑 equals 11 into our formula, giving us 𝑣 is equal to the square root of 32 multiplied by 11. 32 multiplied by 10 is 320. This means that 32 multiplied by 11 is equal to 352. Our value of 𝑣 is the square root of 352.

352 is not a square number, so we need to type this into our calculator and round to the nearest tenth. The square root of 352 is equal to 18.7616 and so on. Rounding to the nearest tenth is the same as rounding to one decimal place. So our deciding number is the first six. If the deciding number is five or greater, we round up. 𝑣 is therefore equal to 18.8 to the nearest tenth. As our units for 𝑣 were feet per second, we can conclude that when the depth is 11 feet, the speed of the wave is 18.8 feet per second.