Question

1. Which Statement Is True About The Product Square Root Of 2(3Square Root Of 2 + Square Root Of 18)?

Math can be daunting for some, but it can also be quite fascinating for those who understand how equations and formulas work. In this blog post, we’ll take a look at one particular equation involving the product of two square roots and determine which statement about it is true. Through our exploration of the equation, you’ll learn a bit more about square roots and why they are so important. So if you’re ready to explore the product of two square roots, let’s get started!

The product is equal to the sum of the two terms

We can easily prove that the product square root of (square root of + square root of ) is equal to the sum of the two terms by expanding both sides.

On the left-hand side, we have:

square root of [(square root of )(square root of )]
= {using the property that the square root of a product is equal to the product of the square roots}
= (square root of )(square root of )
= (square root of + square root of )

On the right-hand side, we have:

(square root of + square root of )(squarerootof+squarerootof)
= {distributing}
= [{squarerootof}+{squarerootof}][{squarerootof}+{sqaurerootof}]
= {expanding brackets and using distributivity again}
= ({sqaurerootof}{sqaurerootof}) + ({sqaurerootof}{sqaurerootof}) + ({sqaurerootof}{sqaurerootof}) + ({sqaurerootof}{sqaurerootOf})
= {cancelling like terms on each side}
= 2({SquareRootOf}{SquareRootOf})
= 2(SquareRootOf+SquareRootOf)

The product is less than the sum of the two terms

The product is less than the sum of the two terms when both square roots are positive and the first term is greater than the second term. This can be seen by rewriting the product as follows:

= ( + )

Since both square roots are positive, we can take the square root of each side to get:

≤ +

And since the first term is greater than the second term, we know that < , so < .

The product is greater than the sum of the two terms

The product of two square roots is always greater than the sum of the two terms. This is because, when you take the square root of a number, you are essentially taking the number that would give you that result when multiplied by itself. So, when you square a number, you are really just multiplying it by itself.

There is not enough information given to determine which statement is true

There is not enough information given in the question to determine which statement is true about the product square root of (square root of + square root of ). We would need to know what value is being squared and added in order to solve for the product.

Conclusion

In conclusion, the statement that is true about the product Square Root Of 2(3Square Root Of 2 + Square Root Of 18) is that it equals 6. This statement can be proven through finding and simplifying all of the square roots present in the equation, then using this knowledge to solve for the final answer. Doing so allows us to find out what value this product actually has, which in this case happens to be 6.

2. Do you have trouble solving equations involving square roots and other mathematical problems? Finding the answer to the statement, “Which statement is true about the product square root of 2(3square root of 2 + square root of 18)?”, can be tricky. But, don’t worry! We’ve got you covered.

Let’s start by breaking down the equation. The product of square root of 2(3square root of 2 + square root of 18) is equal to the expression (2×3)×(2+18). Therefore, the statement is true if and only if the expression evaluates to a number.

To evaluate the expression, we must first simplify it. To simplify the equation, we can use the distributive property, which states that when multiplying a number times a sum, we can multiply the number times each term in the sum. Therefore, the expression simplifies to (2×3)×2 + (2×3)×18.

Next, we can use the commutative property, which states that the order of the factors in a multiplication equation doesn’t matter. Therefore, the expression simplifies to 6×2 + 54, which evaluates to 12 + 54 = 66. Thus, the statement is true.

Now that we’ve found the answer, let’s review what we’ve learned. First, the product of square root of 2(3square root of 2 + square root of 18) is equal to the expression (2×3)×(2+18). Secondly, we can use the distributive and commutative properties to simplify the equation and evaluate it. Lastly, the statement is true if and only if the expression evaluates to a number.

We hope this blog helped you understand the statement, “Which statement is true about the product square root of 2(3square root of 2 + square root of 18)?”. If you’re still having trouble solving equations with square roots and other mathematical problems, don’t hesitate to reach out for help!