Astudent says that the square root of 7 is a rational number because it can be written as [the square root of 7] over 1. is the student correct? explain

Let's start by defining what a rational number is. It is a number that is expressed as a fraction. It could also be in decimal form, but only in circumstances when the decimal places are exact and not continuous or repeating. Let's take for example √7. Its exact value is 2.645751311. The decimals places are random and continuous that's why it can't be expressed into fraction. But if the decimal for is, say, 0.25, that is rational because it can be expressed to 1/4.

Now, the reason where it could be a fraction by using a denominator of 1 is invalid. All whole numbers have a denominator of 1. It is implicitly defined because any number divided by 1 is equal to the number itself. This is not a basis for a characteristic of a rational number. Therefore, the student is incorrect.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.