Simplify the expression by subtracting the radicals.

Question

⬜50-28=6⬜

Answer 1

To simplify the expression by subtracting the radicals, we first need to clarify what the expression involves. It looks like we're dealing with square roots (radicals) and a subtraction of two numbers followed by some radicals.

Assuming the expression involves square roots, rewrite it as follows:

\[ \sqrt{50} - \sqrt{28} = x \]

1. First, simplify the radicals \(\sqrt{50}\) and \(\sqrt{28}\):

   • \(\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}\)
   • \(\sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7}\)

2. Now substituting these back into the expression we have:

\[ 5\sqrt{2} - 2\sqrt{7} \]

This expression \((5\sqrt{2} - 2\sqrt{7})\) cannot be simplified further as both radicals are different.

Thus, \(\sqrt{50} - \sqrt{28}\) simplifies to:

\[ 5\sqrt{2} - 2\sqrt{7} \]

If the original expression was indeed referring to something else or further details are necessary, please provide clarification!

Answer 2

What is the product of the following in simplest radical form?
4√6 . 2√18

Answer 3

To find the product of \( 4\sqrt{6} \) and \( 2\sqrt{18} \), we can follow these steps:

1. Multiply the coefficients (the numbers outside the radicals): \[ 4 \times 2 = 8 \]

2. Multiply the radicals: \[ \sqrt{6} \times \sqrt{18} = \sqrt{6 \times 18} = \sqrt{108} \]

3. Now, simplify \(\sqrt{108}\):

   • First, we can factor \( 108 \) into its prime factors: \[ 108 = 36 \times 3 = 6^2 \times 3 \]
   • Therefore, \[ \sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3} \]

4. Combine the results: Now, we can combine the coefficient with the simplified radical: \[ 8\sqrt{108} = 8 \cdot 6\sqrt{3} = 48\sqrt{3} \]

Thus, the product \( 4\sqrt{6} \cdot 2\sqrt{18} \) in simplest radical form is: \[ \boxed{48\sqrt{3}} \]

Answer 4

Samantha is designing a quilt with right triangles. A large right triangle with a side length of
308 centimeters has smaller right triangles with side lengths of 62 centimeters along it. How many smaller lengths are running along the longer length?
short explanation

Answer 5

To determine how many smaller right triangles with side lengths of 62 centimeters can fit along the longer side of the large right triangle with a side length of 308 centimeters, we simply divide the length of the larger triangle by the length of the smaller triangles.

\[ \frac{308 \text{ cm}}{62 \text{ cm}} = 4.967741935 \]

As we are interested in whole triangles, we take the integer part of this division:

\[ 4 \]

So, 4 smaller triangles of 62 centimeters can fit along the longer side of the large triangle.

A short explanation is that you divide the length of the larger triangle by the length of the smaller triangle to find out how many whole smaller triangles fit along that length.