Squares & Square Roots
The square of 8
What is 64
Estimate the square root of 26.
What is 5.1
In a right triangle with legs of length 3 units and 4 units, what is the length of the hypotenuse?
What is 5
Apply the Pythagorean theorem to find the missing side in a right triangle with legs of length 5 units and 12 units.
What is 13
Calculate the square root of 100 using prime factorization
What is 2x2x5x5
Approximately what is the square root of 150 to the nearest whole number?
What is 12
If one leg of a right triangle is 5 units and the hypotenuse is 13 units, what is the length of the other leg?
What is 12
Solve for the missing side in a right triangle with legs of length 9 units and 12 units using the Pythagorean theorem.
What is 15
Estimate the square root of 7
What is 2.5
Estimate the square root of 200 to one decimal place.
What is 14.1
What is the missing side length in a right triangle with legs of length 6 units and 8 units?
What is 10
How can the Pythagorean theorem help in determining if a triangle is a right triangle or not?
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Estimate the square root of 80
What is 8.9
Estimate the square root of 500 to the nearest tenth
What is 22.4
In a right triangle, if one leg is 12 units and the hypotenuse is 13 units, what is the missing side?
What is 5
A ladder is leaning against a wall. If the ladder is 25 feet long and the base is 24 feet from the wall, how high up the wall does the ladder reach?
What is 7 ft
What is the relationship between the square and square root of a number?
Squares and square roots both concepts are opposite in nature to each other. Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value.
Why is estimating square roots useful in real-life situations?
From the Pythagorean Theorem, we can use square roots to find distances and lengths of sides of triangles in 2 dimensions (or 3 dimensions). This can be useful in all sorts of applications, such as: Architecture & Engineering (finding lengths of trusses to hold up bridges and buildings).
Explain how the Pythagorean theorem can be used to find missing sides in any right triangle.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse). We can apply the theorem to find the missing side length of a right triangle, even when the missing length is one of the shorter sides.
In what real-life scenarios would you need to use the Pythagorean theorem to solve problems?
Examples: To calculate the length of staircase required to reach a window. To find the length of the longest item can be kept in your room. To find the steepness of the hills or mountains. To find the original height of a tree broken due to heavy rain and lying on itself.